Invariant Approximation Results of Generalized Contractive Mappings
|
|
- Olivia Hill
- 5 years ago
- Views:
Transcription
1 Filomat 30:14 (016), DOI 10.98/FIL C Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: Invariant Approximation Results of Generalized Contractive Mappings Ljubomir Ćirić a, Sumit Chandok b, Mujahid Abbas c a Department of Mathematics, University of Belgrade, Serbia. b School of Mathematics, Thapar University, Patiala , Punjab, India. c Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 000, South Africa. Abstract. Abbas, Ali and Salvador [Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 013, 013:43] extended the concept of F contraction mapping introduced in [1], to two mappings. The aim of this paper is to introduce the notion of a generalized F weak contraction mapping and to study sufficient conditions for the existence of common fixed points for such class of mappings. As applications, related invariant approximation results are derived. The results obtained herein unify, generalize and complement various known results in the literature. 1. Introduction and Preliminaries The Banach contraction principle appeared in explicit form in Banach s thesis [3] in 19 where it was used to establish the existence of a solution for an integral equation. Since then, it has become a very popular tool in solving existence problems in many branches of mathematics. Extensions of this principle were obtained either by generalizing the domain of mappings or by extending the contractive condition on the mappings (see, e.g., [1],[],[4]-[] and references mentioned therein). Recently, Wardowski [1] introduced a new type of contractive mapping called F-contraction and proved a fixed point theorem as a generalization of the Banach contraction principle. Abbas et al. ([]) introduced the concept of F contraction with respect to a self mapping and obtained common fixed point results in an ordered metric space. Meinardus [15] was the first who employed fixed point theorem to prove the existence of invariant approximation in Banach spaces. Subsequently, several interesting and valuable results have appeared about invariant approximations ([4], [5], [13] ). Following this research direction, we introduce a notion of generalized F -contraction mappings and obtain common fixed point results employing such contractions. Some results on invariant approximation for such mappings are also obtained which in turn extend and strengthen various known results. In the sequel the letters N, R + and and R will denote the set of all natural numbers, the set of all nonnegative real numbers and the set of all real numbers, respectively. Next we give some definitions which will be used in the sequel. 010 Mathematics Subject Classification. Primary 47H10; Secondary 54H5, 41A50. Keywords. Common fixed point, F-weak contraction mappings, invariant approximations, weakly compatible mappings. Received: 0 November 014; Accepted: 09 July 015 Communicated by Dragan S. Djordjević addresses: lciric@rcub.bg.ac.rs (Ljubomir Ćirić), chansok.s@gmail.com (Sumit Chandok), mujahid.abbas@up.ac.za (Mujahid Abbas)
2 L. Ćirić et al. / Filomat 30:14 (016), Definition 1.1. ([1]) Let Ϝ be the collection of all mappings F : R + R such that (F1) F is strictly increasing, that is, for all α, β R + such that α < β implies that F(α) < F(β); (F) For any sequence {α n } of positive numbers, lim α n = 0 and lim F(α n ) = are equivalent; (F3) There exists k (0, 1) such that lim αk F(α) = 0. α 0 + For examples of mappings satisfying conditions ( F1 F3 ), we refer to [1] and []. Let F be the collection of all mappings F : R + R which satisfy conditions (F1) and (F3). Definition 1.. ([1]) Let (X, d) be a metric space. A map T : X X is said to be F-contraction on X if there exist F Ϝ and τ > 0 such that the following holds: τ + F(d(Tx, Ty)) F(d(x, y)) for all x, y X with Tx Ty. Abbas et al. ([]) extended the above definition to two mappings. Recently, Wardowski and Dung [] used a contractive inequality introduced and investigated by Ćirić [10], [11] and extended the concept of F contraction mappings to F weak contraction mappings as follows: Definition 1.3. Let (X, d) be a metric space. A map T : X X is said to be F-weak contraction on X if there exist F Ϝ and τ > 0 such that for any x, y X with d(tx, Ty) > 0, the following hold: τ + F(d(Tx, Ty)) F(max{d(x, y), d(x, Tx), d(y, Ty), d(x, Ty) + d(y, Tx) }). Every F contraction mapping is F weak contraction but converse does not hold in general ([]). To begin with, we recall the following result of []. Theorem 1.4. Let (X, d) be a complete metric space and T : X X be F-weak contraction. If T or F is continuous, then we have (1) T has a unique fixed point x 1 X. () For all x X, the sequence {T n x} is convergent to x 1. Now, we give the following definition. Definition 1.5. Let (X, d) be a metric space and T, : X X. A mapping T is called F -weak contraction on X if there exist F F and τ > 0 such that for any x, y X with d(tx, Ty) > 0, the following holds: τ + F(d(Tx, Ty)) F(max{d( x, y), d( x, Tx), d( y, Ty), d( x, Ty) + d( y, Tx) }). Definition 1.6. Let (X, d) be a metric space and T, : X X. A mapping T is called F -contraction on (X, d) if there exist F F and τ > 0 such that, for all x, y X satisfying d(tx, Ty) > 0, the following holds: τ + F(d(Tx, Ty)) F(d( x, y)). The following example shows that a mapping T is F -weak contraction but not F -contraction. Example 1.7. Let X = [0, 1], and d(x, y) = x y. Define T, : X X by T(x) = 1 3, x [0, 1 3 ) 1, x [ 1 3, 1) 0, x = 1
3 L. Ćirić et al. / Filomat 30:14 (016), and (x) = 8 10, x [0, 1 3 ) 9 10, x [ 1 3, 1]. Note that T is F -weak contraction when F(t) = ln(t), t (0, + ) and τ = ln but not F -contraction if x = 1 and y = 0. A subset M of a normed space E is said to be (1) convex if M includes every line segment joining any two of its points () z starshaped or starshaped with respect to z M if for any x M and q [0, 1], qz + (1 q)x M. In this case, z is called a star-centre of M. A selfmapping f on M is said to be demiclosed at y if for any sequence {x n } in M with {x n } converges weakly to x M and { f x n } converges to y strongly, then f x = y. Definition 1.8. Let (X, d) be a metric space and f, : X X. The pair ( f, ) is called (a) commuting if f x = f x for all x X (b) compatible if for any {x n } in X with lim f x n = lim x n = t for some t in X, we have lim d( f x n, f x n ) = 0 (c) weakly compatible if they commute at their coincidence points, that is, if f x = f x whenever x = f x. Let f and be two self maps on X. A point x X is called (1) a fixed point of f if f (x) = x; () a common fixed point of and f if x = x = f x; (3) coincidence point of and f if x = f x. The set of all common fixed points ( coincidence points) of and f is denoted by F(, f ) ( C(, T), respectively). Let M be a subset of metric space (X, d). For any x X, define P M (x) = {y M : d(x, y) = d(x, M)}, where d(x, M) = inf{d(x, y) : y M}. The set P M (x) is the set of best approximations of x from M. If for each x X, P M (x) is nonempty, then M is called proximinal. Observe that if M is closed, then P M (x) is also closed. The reader interested in the interplay of fixed points and approximation theory in normed spaces is referred to the pioneer work of Park [18] and Singh ([0]).. Main Results Theorem.1. Let D be a subset of a metric space (X, d) and and T selfmappings of D with T(D) (D). If T(D) is complete, F F is a continuous mapping, T is F -weak contraction mapping on D, then T and have a unique coincidence point. Moreover if (, T) is weakly compatible, then F(T) F( ) is a singleton. Proof. Let x 0 in D be arbitrary. Choose a point x 1 D such that x 1 = Tx 0. This can be done because T(D) (D). As x 1 (D), there exists x D such that x = Tx 1. Continuing this process, having chosen x n in D with (x n ) D, we obtain x n+1 in D such that x n+1 = Tx n. Thus we obtain a sequence {x n } in D such that x n+1 = Tx n for n 0. If there exists some n 0 in N {0} such that Tx n0 = Tx n0 +1, then Tx n0 = x n0 +1 implies that x n0 +1 = Tx n0 +1 and x n0 +1 is coincidence point of and T. We assume that Tx n+1 Tx n for all n in N {0}. Consider F(d(Tx n+1, Tx n )) F(max{d( x n+1, x n ), d( x n+1, Tx n+1 ), d( x n, Tx n ) d( x n+1, Tx n ) + d( x n, Tx n+1 ) = F(max{d(Tx n, Tx n 1 ), d(tx n, Tx n+1 ), d(tx n 1, Tx n ) d(tx n, Tx n ) + d(tx n 1, Tx n+1 ) F(max{d(Tx n, Tx n 1 ), d(tx n, Tx n+1 ), d(tx n 1, Tx n ), d(tx n 1, Tx n ) + d(tx n, Tx n+1 ) = F(max{d(Tx n, Tx n 1 ), d(tx n, Tx n+1 ).
4 L. Ćirić et al. / Filomat 30:14 (016), If for some n 1, max{d(tx n, Tx n 1 ), d(tx n, Tx n+1 )} = d(tx n, Tx n+1 ) then we have F(d(Tx n+1, Tx n )) F(d(Tx n+1, Tx n )) τ < F(d(Tx n+1, Tx n )) a contradiction. Hence max{d(tx n, Tx n 1 ), d(tx n, Tx n+1 )} = d(tx n, Tx n 1 ) for all n 1. Thus, we have F(d(Tx n+1, Tx n )) F(d(Tx n, Tx n 1 )) τ for all n 1. This further implies that F(d(Tx n+1, Tx n )) F(d(Tx 1, Tx 0 )) nτ for all n 1. On taking limit as n, we have lim F(d(Tx n+1, Tx n )) =. We now show that lim d(tx n+1, Tx n ) = 0. Assume on contrary that lim d(tx n+1, Tx n ) = α 0. Using Archmidean property of real numbers, there exists some α 1 R + such that 0 < α 1 < α. By nondecreasing property of F, we obtain that F(α 1 ) <, a contradiction. Hence lim d(tx n+1, Tx n ) = 0. By (F3), there exists k (0, 1) such that lim (d(tx n+1, Tx n )) k F(d(Tx n+1, Tx n )) = 0. As F(d(Tx n+1, Tx n )) F(d(Tx 1, Tx 0 )) nτ, so and hence (d(tx n+1, Tx n )) k [F(d(Tx n+1, Tx n )) F(d(Tx 1, Tx 0 ))] (d(tx n+1, Tx n )) k nτ 0, lim (d(tx n+1, Tx n )) k n = 0. Thus, there exists n 1 N such that (d(tx n+1, Tx n )) k n 1 for all n n 1. That is, d(tx n+1, Tx n ) 1 n n 1. Therefore for all m > n 1, we have d(tx m, Tx n ) d(tx m, Tx m 1 ) d(tx n+1, Tx n ) < d(tx i+1, Tx i ) i=n i=n 1 i 1/k < n 1 k for all This proves that {Tx n } is a Cauchy sequence in g(x). As x n = Tx n 1, { x n } is also a Cauchy sequence in T(D). By the completeness of T(D), there is some w T(D) (D) such that lim x n+1 = lim Tx n = w. Let z D be such that (z) = w, that is, lim x n+1 = lim Tx n = z. (1) Let us assume that d(tz, Tx n ) > 0 and d( z, Tz) > 0. As T is a weak F-contraction, we have F(d(Tz, Tx n )) F(max{d( z, x n ), d( z, Tz), d( x n, Tx n ), d( z, Tx n) + d( x n, Tz). ()
5 L. Ćirić et al. / Filomat 30:14 (016), Then from (1) and () there is a sufficiently large n 0, such that F(d(Tz, Tx n )) F(d(Tz, z)) τ, (3) for all n n 0. Note that if lim d(tz, Tx n ) = d(tz, z) > 0, then by (F), lim F(d(Tz, Tx n )). Now, taking the limit as n in the above inequality (3), we get, as lim F(d(Tz, Tx n)) = F(d(Tz, z)), F(d(Tz, z)) F(d(Tz, z)) τ. Hence we have τ 0, a contradiction with the assumption τ > 0. Therefore, our supposition d( z, Tz) > 0 was wrong. Thus d( z, Tz) = 0. Hence Tz = z. So we proved that z is a coincidence point of T and. Now suppose that T and are weakly compatible. Since w = T(z) = (z), then T(w) = T( (z)) = (T(z)) = (w). Now we show that (w) = w. If T(z) T(w), then we have d( z, Tw) + d( w, Tz) F(d(T(z), T(w))) F(max{d( z, w), d( z, Tz), d( w, Tw), d(tz, Tw) + d(tw, Tz) = F(max{d(Tz, Tw), = F(d(Tz, Tw)) τ, a contradiction. Hence T(z) = T(w) = (w) = w. If z 1, z are two common fixed points of T and such that z 1 z, then we have F(d(z 1, z )) = F(d(T(z 1 ), T(z ))) a contradiction. Hence z 1 = z. F(max{d( z 1, z ), d( z 1, Tz 1 ), d( z, Tz ), d( z 1, Tz ) + d( z, Tz 1 ) = F(max{d(z 1, z ), d(z 1, z 1 ), d(z, z ), d(z 1, z ) + d(z, z 1 ) = F(d(z 1, z )) τ. Corollary.. Let D be a subset of a metric space (X, d) and and T self-mappings on D with T(D) (D). If T(D) is complete, F F is a continuous mapping, T is F -contraction mapping on D, then T and have a unique coincidence point in D. Moreover if (, T) is weakly compatible, then F(T) F( ) is a singleton. If =identity mapping, then we have the following results. Corollary.3. Let D be a nonempty subset of a metric space (X, d) and T : D D. If T(D) D, T(D) is complete, F F is a continuous mapping, and T is an F-weak contraction, then F(T) is singleton. Corollary.4. Let D be a nonempty subset of a metric space (X, d) and T : D D. If T(D) D, T(D) is complete, F F is a continuous mapping, and T is an F-contraction mapping, then F(T) is a singleton. As an application of Corollary.3, we obtain the following general result. Theorem.5. Let D be a nonempty subset of a metric space (X, d) and, T : D D. If F( ) is nonempty, T(F( )) F( ), T(D) is complete, F F is a continuous mapping, and T is F -weak contraction, then F(, T) is a singleton.
6 Proof. Let x, y F( ). Note that L. Ćirić et al. / Filomat 30:14 (016), d( x, Ty) + d( y, Tx) F(d(Tx, Ty)) F(max{d( x, y), d( x, Tx), d( y, Ty), d(x, Ty) + d(y, Tx) = F(max{d(x, y), d(x, Tx), d(y, Ty),. Hence T is an F weak contraction on F( ). The completeness of T(D) implies the completeness of T(F( )). It follows from Corollary.3 that F(, T) = F( ) F(T) is singleton. In the sequel, we assume that D is a q-starshaped subset of a normed space E and, T : D D. Define δ( x, Ty) := inf{ x T k y : 0 k 1} for all x, y D where T k x := ktx + (1 k)q. For a subset D of a normed space E, D w denotes weak closure of D in E Definition.6. Let X be a normed linear space and T, : X X. A mapping T is called generalized F -nonexpansive on X if there exist F F and τ > 0 such that for any x, y X with d(tx, Ty) > 0, we have F( Tx Ty ) F(max{ x y, δ( x, Tx), δ( y, Ty), δ( x, Ty), δ( y, Tx). Theorem.7. Let D be a subset of a normed space E and, T : D D. If F( ) is q-starshaped, T(F( )) F( ), T(D) is compact, T is continuous and generalized F -nonexpansive on D, F F is a continuous mapping, then F(, T) is nonempty. Moreover, if we replace T(F( )) F( ) with T(F( )) w F( ), compactness of T(D) with weak compactness of T(D) and continuity of T with demiclosedness of T at zero, then the same conclusion holds provided that E is a Banach space. Proof. Let {λ n } be a sequence in (0, 1) such that λ n 1 as n. For each n 1, define T n x = λ n Tx + (1 λ n )q for all x F( ). As F( ) is q-starshaped and T(F( )) F( ), so we have T n (F( )) F( ) for each n 1. Note that F( T n x T n y ) = F( λ n Tx + (1 λ n )q λ n Ty (1 λ n )q ) = F( λ n (Tx Ty) ). Since F is strictly increasing and λ n < 1 for each n 1, therefore F( T n x T n y ) < F( (Tx Ty) ) < F(max{ x y, δ( x, Tx), δ( y, Ty), δ( x, Ty), δ( y, Tx) < F(max{ x y, x T n x, y T n y, x T n y, y T n x holds for all x, y F( ). As T(D) is compact, so T n (D) is compact for each n 1. Thus T n (D) is complete for each n 1. It follows from Theorem.5 that for each n 1, F(, T n ) = F( ) F(T n ) = {x n } for some x n F( ). Since T(D) is compact, there exists a subsequence {Tx nk } of {Tx n } such that Tx nk z T(D). Since {Tx n } is a sequence in T(F( )), then z T(F( )) F( ). Moreover, x nk = T nk x nk = λ nk Tx nk + (1 λ nk )q z. As T is continuous on D, we have Tz = z. Next, assume that T(D) w is weakly compact and T is demiclosed at zero. Thus there exists a subsequence {Tx nk } of {Tx n } such that Tx nk w z T(F( )) w. Since {Tx n } is a sequence in T(F( )), then
7 L. Ćirić et al. / Filomat 30:14 (016), z T(F( )) w F( ). From the boundedness of {Tx nk }, we conclude that {x xnk } is bounded too. As λ nk 1 and x nk Tx nk = x nk Tx nk = (1 λ nk )q + λ nk Tx nk Tx nk (1 λ nk ) q Tx nk (1 λ nk ) ( q + Tx nk ), for each k 1. We have x nk Tx nk w 0. It follows from the demiclosedness of T at zero that z Tz = ( T)z = 0 and hence Tz = z. The result follows. Let M be a nonempty subset of a metric space (X, d). Suppose that C = P M (u) C f M (u), where C M (u) = {x M : x P M (u)}. Corollary.8. Let E be a normed linear space and T, self mappings of E. If u E, D G, G = D F( ) is q- starshaped, T(G) G, T(D) is compact, and T is continuous generalized F -nonexpansive on D, F F is a continuous mapping, then P M (u) F(, T) is nonempty. Moreover, if we replace T(G) G with T(G) w G, compactness of T(D) with weak compactness of T(D) and continuity of T with demiclosedness of T at zero, then the same conclusion holds provided that E is a Banach space. Corollary.9. Let E be a normed linear space and T, f self mappings of X. If u E, D P M (u), G = D F( f ) is q- starshaped, T(G) G, T(D) is compact and T is continuous generalized F -nonexpansive on D, F F is a continuous mapping, then P M (u) F( f, T) is nonempty. Moreover, if we replace T(G) G with T(G) w G, compactness of T(D) with weak compactness of T(D) and continuity of T with demiclosedness of f T at zero, then the same conclusion holds provided that E is a Banach space. Let G 0 denotes the class of closed convex subsets of a normed space X containing 0. For M G 0 and p X, let M p = {x M : x p }. Then P M (p) M p G 0 (see [4], [17]). Theorem.10. Let E be a normed linear space and T, self mappings on X. If p E and M G 0 such that T(M p ) M, T(M p ) is compact, and Tx p x p for all x M p, then P M (p) is nonempty, closed and convex with T(P M (p)) P M (p). If, in addition, D is a subset of P M (p), G = D F( ) is q-starshaped, T(G) G and T is continuous generalized F -nonexpansive on D, F F is a continuous mapping, then P M (p) F(, T) is nonempty. Moreover if we replace compactness of T(M p ) with weak compactness of T(M p ) w, T(G) G with T(G) w G and continuity of T with demiclosedness of T at 0, then the same conclusion holds provided that E is a Banach space. Proof. If p M then the result follows. Assume that p M. If x M\M p, then x > p and hence p x x p > p d(p, M). Thus α = d(p, M) p. As T(M p ) is compact so by the continuity of norm, there exists z T(M p ) such that β = d(p, cl T(M p )) = z p. On the other hand, if T(M p ) w is weakly compact, then by Lemma 5.5 in ([0]), there exists z T(M p ) w such that β = d(p, T(M p ) w ) = z p. Thus in both cases, we have α = d(p, M) d(p, T(M p )) = β = d(p, T(M p )) Tx p x p
8 for all x M p. Therefore α = β = d(p, M), that is, d(p, M) = d(p, T(M p )) = p z L. Ćirić et al. / Filomat 30:14 (016), and z P M (P). Hence P M (p) is nonempty. The closedness and convexity of P M (p) follows from that of M. Now we prove that T(P M (p)) P M (p). If y T(P M (p)). Then y = Tx for some x P M (p). Since p y = p Tx p x = d(p, M). Therefore y P M (p) M p. Now T(P M (p)) M gives that y M. The compactness of T(M p ) (weak compactness of T(M p ) w, respectively) implies that T(D) compact (respectively, T(D) w is weakly compact). Hence the result follows from Corollary.9. Example.11. Let M = [0, 1]. Define T, :M M by T(x) = and (x) = x. Note that 0, x [0, 1 ) 1 8, x [ 1, 1] τ + F(d(Tx, Ty)) F(max{d( x, y), d( x, Tx), d( y, Ty), d( x, Ty) + d( y, Tx) }) holds with F(t) = ln(t), t (0, + ) and τ = ln 1.5. Moreover 0 is common fixed point of T and. Remarks ) It must be noted that the assumption of linearity or affinity for I is necessary in almost all known results dealing with common fixed points of maps T, and I when T is I-nonexpansive under the conditions of commuting, weakly commuting, R-subweakly commuting, compatibility or Banach operator pairs (see [4]-[9], [14] and the literature cited therein), but our results in this paper are independent of the linearity or affinity condition on I. ) In [], it was shown that from different types of F-weak contractions, one can obtain the variety of well-known contractions. Using the concept the of Wardowski [1], we introduce the F -weak contraction mappings by omitting condition (F) which was assumed in [1, ]. Also, in Example 1.7, we showed that F -contraction is F -weak contraction but not conversely. Therefore, the obtained results generalize and extend many of the well-known results existing in the literature to F -weak contraction mappings. Acknowledgement: The authors thank editor and reviewers for their valuable suggestions that helped us to improve the final version of the paper. References [1] M. Abbas, B. Ali and S. Romaguera, Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces, Abstract and Applied Analysis, 014(014), Article 39195, 5 pages. [] M. Abbas, B. Ali and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 013, 013:43. [3] S. Banach, Sur les op erations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3(19), [4] M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory 85(1996), [5] M. A. Al-Thagafi and N. Shahzad, Noncommuting self-maps and invariant approximations, Nonlinear Anal. 64(006), [6] M. A. Al-Thagafi and N. Shahzad, Banach operator pairs, common fixed points, invariant approximations, and -nonexpansive multimaps, Nonlinear Analysis 69 (008), [7] S. Chandok, Some common fixed point theorems for generalized nonlinear contractive mappings, Computers Math. Appl. 6 (10)(011), [8] S. Chandok, Common fixed points, invariant approximation and generalized weak contractions, Internat. J. Math. Math. Sci. Vol. 01 (01) Article ID
9 L. Ćirić et al. / Filomat 30:14 (016), [9] S. Chandok and T. D. Narang, Some common fixed point theorems for Banach operator pairs with applications in best approximation, Nonlinear Anal. 73(010), [10] L. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. 1 (6) (1971), [11] L. B. Ćirić, Fixed-points for generalized multi-valued mappings, Mat. Vesnik 9 (4) (197), [1] L. B. Ćirić, A generalization of Banach s contraction principle, Proc. Amer. Math. Soc. 45 (1974), [13] L. Habiniak, Fixed point theorems and invariant approximation, J. Approx. Theory 56(1989), [14] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83(1976), [15] G. Meinardus, Invarianz bei linearn approximation, Arch. Ration. Mech. Anal. 14, (1963). [16] T. D. Narang and S. Chandok, Fixed points and best approximation in metric spaces, Indian J. Math. 51(009), [17] T. D. Narang and S. Chandok, Common fixed points and invariant approximation of R-subweakly commuting maps in convex metric spaces, Ukrainian Math. J. 6 (010), [18] S. Park, Best approximations, inward sets and fixed points, Progress in Approximation Theory, pp , Acedemic Press, Inc (1991). [19] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47(001), [0] S. P. Singh, B. Watson and P. Srivastava, Fixed Point Theory and Best Approximation: The KKM-map Principle, Kluwer Academic Publishers. Dordrecht (1997). [1] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (01), 11 pages. [] D. Wardowski and N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstratio Math. 67(1)(014),
Some Fixed Point Results for the Generalized F -suzuki Type Contractions in b-metric Spaces
Sahand Communications in Mathematical Analysis (SCMA) Vol. No. (208) 8-89 http://scma.maragheh.ac.ir DOI: 0.2230/scma.208.52976.55 Some Fixed Point Results for the Generalized F -suzuki Type Contractions
More informationOn Common Fixed Point and Approximation Results of Gregus Type
International Mathematical Forum, 2, 2007, no. 37, 1839-1847 On Common Fixed Point and Approximation Results of Gregus Type S. Al-Mezel and N. Hussain Department of Mathematics King Abdul Aziz University
More informationCommon fixed point of -approximative multivalued mapping in partially ordered metric space
Filomat 7:7 (013), 1173 118 DOI 1098/FIL1307173A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://wwwpmfniacrs/filomat Common fixed point of -approximative
More informationA Suzuki-Type Common Fixed Point Theorem
Filomat 31:10 (017), 951 956 https://doi.org/10.98/fil1710951c Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Suzuki-Type Common
More informationTwo-Step Iteration Scheme for Nonexpansive Mappings in Banach Space
Mathematica Moravica Vol. 19-1 (2015), 95 105 Two-Step Iteration Scheme for Nonexpansive Mappings in Banach Space M.R. Yadav Abstract. In this paper, we introduce a new two-step iteration process to approximate
More informationFixed Points of Multivalued Quasi-nonexpansive Mappings Using a Faster Iterative Process
Fixed Points of Multivalued Quasi-nonexpansive Mappings Using a Faster Iterative Process Safeer Hussain KHAN Department of Mathematics, Statistics and Physics, Qatar University, Doha 73, Qatar E-mail :
More informationBest proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces
An. Şt. Univ. Ovidius Constanţa Vol. 20(3), 2012, 51 64 Best proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces Erdal Karapınar Abstract In this manuscript, the existence
More information1 Introduction and preliminaries
Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 5: (0), 5 3 DOI: 0.98/FIL05D MULTIVALUED GENERALIZATIONS OF THE KANNAN FIXED POINT THEOREM
More informationCommon fixed point of multivalued mappings in ordered generalized metric spaces
Filomat 6:5 (01), 1045 1053 DOI 10.98/FIL105045A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Common fixed point of multivalued
More informationConvergence to Common Fixed Point for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense in Banach Spaces
Mathematica Moravica Vol. 19-1 2015, 33 48 Convergence to Common Fixed Point for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense in Banach Spaces Gurucharan Singh Saluja Abstract.
More informationA Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity
Mathematica Moravica Vol. 10 (2006), 55 60 A Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity I. Kubiaczyk and Bhavana Deshpande Abstract. In this paper, we prove a common
More informationINVARIANT APPROXIMATIONS, GENERALIZED I-CONTRACTIONS, AND R-SUBWEAKLY COMMUTING MAPS
INVARIANT APPROXIMATION, GENERALIZED I-CONTRACTION, AND R-UBWEAKLY COMMUTING MAP NAEER HAHZAD Received 11 May 004 and in revised form 3 August 004 We present common fixed point theory for generalized contractive
More informationBulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp
Bulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp 1125-1135. COMMON FIXED POINTS OF A FINITE FAMILY OF MULTIVALUED QUASI-NONEXPANSIVE MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES A. BUNYAWAT
More informationConvergence of three-step iterations for Ciric-quasi contractive operator in CAT(0) spaces
Acta Univ. Sapientiae, Mathematica, 7, 1 (15) 89 15 DOI: 1.1515/ausm-15-6 Convergence of three-step iterations for Ciric-quasi contractive operator in CAT() spaces Gurucharan S. Saluja Department of Mathematics,
More informationFixed Point Theorem for Cyclic (µ, ψ, φ)-weakly Contractions via a New Function
DOI: 10.1515/awutm-2017-0011 Analele Universităţii de Vest, Timişoara Seria Matematică Informatică LV, 2, 2017), 3 15 Fixed Point Theorem for Cyclic µ, ψ, φ)-weakly Contractions via a New Function Muaadh
More informationInternational Journal of Scientific & Engineering Research, Volume 7, Issue 12, December-2016 ISSN
1750 Approximation of Fixed Points of Multivalued Demicontractive and Multivalued Hemicontractive Mappings in Hilbert Spaces B. G. Akuchu Department of Mathematics University of Nigeria Nsukka e-mail:
More informationFixed Point Theorems for -Monotone Maps on Partially Ordered S-Metric Spaces
Filomat 28:9 (2014), 1885 1898 DOI 10.2298/FIL1409885D Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Theorems for
More informationCommon fixed points of generalized contractive multivalued mappings in cone metric spaces
MATHEMATICAL COMMUNICATIONS 365 Math. Commun., Vol. 14, No., pp. 365-378 (009) Common fixed points of generalized contractive multivalued mappings in cone metric spaces Mujahid Abbas 1,, B. E. Rhoades
More informationFixed Point Theorem in Cone B-Metric Spaces Using Contractive Mappings
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 7 (2017), pp. 2997-3004 Research India Publications http://www.ripublication.com Fixed Point Theorem in Cone B-Metric Spaces
More informationCONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
International Journal of Analysis and Applications ISSN 2291-8639 Volume 8, Number 1 2015), 69-78 http://www.etamaths.com CONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
More informationCommon Fixed Point Theorems for Six Mappings Satisfying Almost Generalized (S, T)-Contractive Condition in Partially Ordered Metric Spaces
Annals of Pure Applied Mathematics Vol. 1, No., 016, 143-151 ISSN: 79-087X (P), 79-0888(online) Published on 7 November 016 www.researchmathsci.org Annals of Common Fixed Point Theorems for Six Mappings
More informationCommon fixed point theorem for nonexpansive type single valued mappings
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 45-51 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.293 Common fixed point theorem for nonexpansive type single valued mappings Pankaj
More informationIntegral type Fixed point Theorems for α-admissible Mappings Satisfying α-ψ-φ-contractive Inequality
Filomat 3:12 (216, 3227 3234 DOI 1.2298/FIL1612227B Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Integral type Fixed point Theorems
More informationOn Fixed Point Results for Matkowski Type of Mappings in G-Metric Spaces
Filomat 29:10 2015, 2301 2309 DOI 10.2298/FIL1510301G Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On Fixed Point Results for
More informationFixed Points of Multivalued Non-Linear F -Contractions with Application to Solution of Matrix Equations
Filomat 31:11 (017), 3319 3333 https://doi.org/10.98/fil1711319i Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Points of
More informationCommon fixed points of two generalized asymptotically quasi-nonexpansive mappings
An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) Tomul LXIII, 2017, f. 2 Common fixed points of two generalized asymptotically quasi-nonexpansive mappings Safeer Hussain Khan Isa Yildirim Received: 5.VIII.2013
More informationResearch Article Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces
Abstract and Applied Analysis, Article ID 391952, 5 pages http://dx.doi.org/10.1155/2014/391952 Research Article Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed
More informationStrong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1
Applied Mathematical Sciences, Vol. 2, 2008, no. 19, 919-928 Strong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1 Si-Sheng Yao Department of Mathematics, Kunming Teachers
More informationHARDY-ROGERS-TYPE FIXED POINT THEOREMS FOR α-gf -CONTRACTIONS. Muhammad Arshad, Eskandar Ameer, and Aftab Hussain
ARCHIVUM MATHEMATICUM (BRNO) Tomus 5 (205), 29 4 HARDY-ROGERS-TYPE FIXED POINT THEOREMS FOR α-gf -CONTRACTIONS Muhammad Arshad, Eskandar Ameer, and Aftab Hussain Abstract. The aim of this paper is to introduce
More informationAlfred O. Bosede NOOR ITERATIONS ASSOCIATED WITH ZAMFIRESCU MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES
F A S C I C U L I M A T H E M A T I C I Nr 42 2009 Alfred O. Bosede NOOR ITERATIONS ASSOCIATED WITH ZAMFIRESCU MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES Abstract. In this paper, we establish some fixed
More informationFIXED POINTS AND CYCLIC CONTRACTION MAPPINGS UNDER IMPLICIT RELATIONS AND APPLICATIONS TO INTEGRAL EQUATIONS
SARAJEVO JOURNAL OF MATHEMATICS Vol.1 (23) (214), 257 27 DOI: 1.5644/SJM.1.2.11 FIXED POINTS AND CYCLIC CONTRACTION MAPPINGS UNDER IMPLICIT RELATIONS AND APPLICATIONS TO INTEGRAL EQUATIONS HEMANT KUMAR
More informationFixed point theorems of nondecreasing order-ćirić-lipschitz mappings in normed vector spaces without normalities of cones
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 18 26 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa Fixed point theorems of nondecreasing
More informationComputers and Mathematics with Applications
Computers and Mathematics with Applications 64 (2012) 643 650 Contents lists available at SciVerse ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa
More informationMultiplicative metric spaces and contractions of rational type
Advances in the Theory of Nonlinear Analysis and its Applications 2 (2018) No. 4, 195 201. https://doi.org/10.31197/atnaa.481995 Available online at www.atnaa.org Research Article Multiplicative metric
More informationA fixed point theorem for (µ, ψ)-generalized f-weakly contractive mappings in partially ordered 2-metric spaces
Mathematica Moravica Vol. 21, No. 1 (2017), 37 50 A fixed point theorem for (µ, ψ)-generalized f-weakly contractive mappings in partially ordered 2-metric spaces Nguyen Trung Hieu and Huynh Ngoc Cam Abstract.
More informationCONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES. Jong Soo Jung. 1. Introduction
Korean J. Math. 16 (2008), No. 2, pp. 215 231 CONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES Jong Soo Jung Abstract. Let E be a uniformly convex Banach space
More informationExistence and data dependence for multivalued weakly Ćirić-contractive operators
Acta Univ. Sapientiae, Mathematica, 1, 2 (2009) 151 159 Existence and data dependence for multivalued weakly Ćirić-contractive operators Liliana Guran Babeş-Bolyai University, Department of Applied Mathematics,
More informationRemarks on Some New Fixed Point Theorems for Contractive and Nonexpansive Mappings
Filomat 3:0 (07), 6483 649 https://doi.org/0.98/fil70483p Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Remarks on Some New Fixed
More informationCommon fixed points of two maps in cone metric spaces
Rendiconti del Circolo Matematico di Palermo 57, 433 441 (2008) DOI: 10.1007/s12215-008-0032-5 Akbar Azam Muhammad Arshad Ismat Beg Common fixed points of two maps in cone metric spaces Received: July
More informationA fixed point theorem for F-Khan-contractions on complete metric spaces and application to integral equations
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., (27), 4564 4573 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa A fixed point theorem for F-Khan-contractions
More informationFixed point results for generalized multi-valued contractions
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 8 (2015), 909 918 Research Article Fixed point results for generalized multi-valued contractions Jamshaid Ahmad a,, Nawab Hussain b, Abdul Rahim
More informationFuzzy fixed point of multivalued Ciric type fuzzy contraction mappings in b-metric spaces
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume, Number (06), pp. 307-36 Research India Publications http://www.ripublication.com Fuzzy fixed point of multivalued Ciric type fuzzy
More informationFixed points of Ćirić quasi-contractive operators in normed spaces
Mathematical Communications 11(006), 115-10 115 Fixed points of Ćirić quasi-contractive operators in normed spaces Arif Rafiq Abstract. We establish a general theorem to approximate fixed points of Ćirić
More informationBhavana Deshpande COMMON FIXED POINT RESULTS FOR SIX MAPS ON CONE METRIC SPACES WITH SOME WEAKER CONDITIONS. 1. Introduction and preliminaries
F A S C I C U L I M A T H E M A T I C I Nr 43 2010 Bhavana Deshpande COMMON FIXED POINT RESULTS FOR SIX MAPS ON CONE METRIC SPACES WITH SOME WEAKER CONDITIONS Abstract. The existence of coincidence points
More informationA fixed point theorem for a Ćirić-Berinde type mapping in orbitally complete metric spaces
CARPATHIAN J. MATH. 30 (014), No. 1, 63-70 Online version available at http://carpathian.ubm.ro Print Edition: ISSN 1584-851 Online Edition: ISSN 1843-4401 A fixed point theorem for a Ćirić-Berinde type
More informationFixed Points Results via Simulation Functions
Filomat 30:8 (2016), 2343 2350 DOI 10.2298/FIL1608343K Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Points Results via
More informationC q -COMMUTING MAPS AND INVARIANT APPROXIMATIONS
C q -COMMUTING MAPS AND INVARIANT APPROXIMATIONS N. HUSSAIN AND B. E. RHOADES Received 20 December 2005; Revised 29 March 2006; Accepted 4 April 2006 We obtain common fixed point results for generalized
More informationPythagorean Property and Best Proximity Pair Theorems
isibang/ms/2013/32 November 25th, 2013 http://www.isibang.ac.in/ statmath/eprints Pythagorean Property and Best Proximity Pair Theorems Rafa Espínola, G. Sankara Raju Kosuru and P. Veeramani Indian Statistical
More informationOn a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis
Available online at wwwtjnsacom J Nonlinear Sci Appl 9 (2016), 2553 2562 Research Article On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis Wutiphol
More informationCONVERGENCE THEOREMS FOR MULTI-VALUED MAPPINGS. 1. Introduction
CONVERGENCE THEOREMS FOR MULTI-VALUED MAPPINGS YEKINI SHEHU, G. C. UGWUNNADI Abstract. In this paper, we introduce a new iterative process to approximate a common fixed point of an infinite family of multi-valued
More informationReich Type Contractions on Cone Rectangular Metric Spaces Endowed with a Graph
Theory and Applications of Mathematics & Computer Science 4 (1) (2014) 14 25 Reich Type Contractions on Cone Rectangular Metric Spaces Endowed with a Graph Satish Shukla Department of Applied Mathematics,
More informationOn the Convergence of Ishikawa Iterates to a Common Fixed Point for a Pair of Nonexpansive Mappings in Banach Spaces
Mathematica Moravica Vol. 14-1 (2010), 113 119 On the Convergence of Ishikawa Iterates to a Common Fixed Point for a Pair of Nonexpansive Mappings in Banach Spaces Amit Singh and R.C. Dimri Abstract. In
More informationCommon Fixed Point Theorems for Ćirić-Berinde Type Hybrid Contractions
International Journal of Mathematical Analysis Vol. 9, 2015, no. 31, 1545-1561 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.54125 Common Fixed Point Theorems for Ćirić-Berinde Type
More informationKrasnoselskii-Mann Method for Multi-valued Non-Self Mappings in CAT(0) Spaces
Filomat 31:14 (2017), 4629 4640 https://doi.org/10.2298/fil1714629t Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Krasnoselskii-Mann
More informationIstratescu-Suzuki-Ćirić-type fixed points results in the framework of G-metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 016), 6077 6095 Research Article Istratescu-Suzuki-Ćirić-type fixed points results in the framework of G-metric spaces Mujahid Abbas a,b, Azhar
More informationFixed points and functional equation problems via cyclic admissible generalized contractive type mappings
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 1129 1142 Research Article Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings
More informationStrong convergence of multi-step iterates with errors for generalized asymptotically quasi-nonexpansive mappings
Palestine Journal of Mathematics Vol. 1 01, 50 64 Palestine Polytechnic University-PPU 01 Strong convergence of multi-step iterates with errors for generalized asymptotically quasi-nonexpansive mappings
More informationON WEAK CONVERGENCE THEOREM FOR NONSELF I-QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
BULLETIN OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 69-75 Former BULLETIN OF SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) ON WEAK CONVERGENCE
More informationCONVERGENCE THEOREMS FOR STRICTLY ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN HILBERT SPACES. Gurucharan Singh Saluja
Opuscula Mathematica Vol 30 No 4 2010 http://dxdoiorg/107494/opmath2010304485 CONVERGENCE THEOREMS FOR STRICTLY ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN HILBERT SPACES Gurucharan Singh Saluja Abstract
More informationWeak and strong convergence theorems of modified SP-iterations for generalized asymptotically quasi-nonexpansive mappings
Mathematica Moravica Vol. 20:1 (2016), 125 144 Weak and strong convergence theorems of modified SP-iterations for generalized asymptotically quasi-nonexpansive mappings G.S. Saluja Abstract. The aim of
More informationA fixed point theorem on compact metric space using hybrid generalized ϕ - weak contraction
Theoretical Mathematics & Applications, vol. 4, no. 4, 04, 9-8 ISSN: 79-9687 (print), 79-9709 (online) Scienpress Ltd, 04 A fixed point theorem on compact metric space using hybrid generalized ϕ - weak
More informationConvergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 2016), 5119 5135 Research Article Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense Gurucharan
More informationBest proximity problems for Ćirić type multivalued operators satisfying a cyclic condition
Stud. Univ. Babeş-Bolyai Math. 62(207), No. 3, 395 405 DOI: 0.2493/subbmath.207.3. Best proximity problems for Ćirić type multivalued operators satisfying a cyclic condition Adrian Magdaş Abstract. The
More informationFIXED POINT THEOREMS AND CHARACTERIZATIONS OF METRIC COMPLETENESS. Tomonari Suzuki Wataru Takahashi. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 8, 1996, 371 382 FIXED POINT THEOREMS AND CHARACTERIZATIONS OF METRIC COMPLETENESS Tomonari Suzuki Wataru Takahashi
More informationOn the effect of α-admissibility and θ-contractivity to the existence of fixed points of multivalued mappings
Nonlinear Analysis: Modelling and Control, Vol. 21, No. 5, 673 686 ISSN 1392-5113 http://dx.doi.org/10.15388/na.2016.5.7 On the effect of α-admissibility and θ-contractivity to the existence of fixed points
More informationF -contractions of Hardy Rogers type and application to multistage decision processes
Nonlinear Analysis: Modelling and Control, Vol. 2, No. 4, 53 546 ISSN 392-53 http://dx.doi.org/0.5388/na.206.4.7 F -contractions of Hardy Rogers type and application to multistage decision processes Francesca
More informationResearch Article Common Fixed Point and Approximation Results for Noncommuting Maps on Locally Convex Spaces
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009, Article ID 207503, 14 pages doi:10.1155/2009/207503 Research Article Common Fixed Point and Approximation Results for Noncommuting
More informationNew Coupled Common Fixed Point for Four Mappings satisfying Rational Contractive Expression
New Coupled Common Fixed Point for Four Mappings satisfying Rational Contractive Expression H K Nashine 1, A Gupta 2 1 Department of Mathematics, Amity University, Manth Kharora, Raipur-(Chhattisgarh),
More informationOn the Existence of Bounded Solutions to a Class of Nonlinear Initial Value Problems with Delay
Filomat : (27, 25 5 https://doi.org/.2298/fil725a Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On the Existence of Bounded Solutions
More informationFIXED POINT THEORY FOR QUASI-CONTRACTION MAPS IN b-metric SPACES
Fixed Point Theory, 15(2014), No. 2, 351-358 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html FIXED POINT THEORY FOR QUASI-CONTRACTION MAPS IN b-metric SPACES A. AMINI-HARANDI Department of Mathematics,
More informationarxiv: v1 [math.fa] 9 Mar 2009
Two Fixed-Point Theorems For Special Mappings A. Beiranvand, S. Moradi, M. Omid and H. Pazandeh arxiv:0903.504v [math.fa] 9 Mar 009 Faculty of Science, Department of Mathematics Arak University, Arak,
More informationCommon Fixed Point Results in S-metric Spaces
Journal of Advances in Applied Mathematics, Vol. 4, No. 2, April 2019 https://dx.doi.org/10.22606/jaam.2019.42002 45 Common Fixed Point Results in S-metric Spaces Jierong Yao * and Liping Yang School of
More informationSome Fixed Point Results for (α, β)-(ψ, φ)-contractive Mappings
Filomat 28:3 214), 635 647 DOI 12298/FIL143635A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://wwwpmfniacrs/filomat Some Fixed Point Results for α, β)-ψ,
More informationApplicable Analysis and Discrete Mathematics available online at
Applicable Analysis and Discrete Mathematics available online at http://pefmath.etf.bg.ac.yu Appl. Anal. Discrete Math. 3 (2009), 236 241. doi:10.2298/aadm0902236a BANACH CONTRACTION PRINCIPLE ON CONE
More informationResearch Article Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces
Abstract and Applied Analysis Volume 2012, Article ID 435790, 6 pages doi:10.1155/2012/435790 Research Article Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly
More informationSome common fixed points of multivalued mappings on complex-valued metric spaces with homotopy result
Available online at wwwisr-publicationscom/jnsa J Nonlinear Sci Appl 10 (2017) 3381 3396 Research Article Journal Homepage: wwwtjnsacom - wwwisr-publicationscom/jnsa Some common fixed points of multivalued
More informationSome Fixed Point Theorems for G-Nonexpansive Mappings on Ultrametric Spaces and Non-Archimedean Normed Spaces with a Graph
J o u r n a l of Mathematics and Applications JMA No 39, pp 81-90 (2016) Some Fixed Point Theorems for G-Nonexpansive Mappings on Ultrametric Spaces and Non-Archimedean Normed Spaces with a Graph Hamid
More informationOccasionally Weakly Compatible Mapping in Cone Metric Space
Applied Mathematical Sciences, Vol. 6, 2012, no. 55, 2711-2717 Occasionally Weakly Compatible Mapping in Cone Metric Space Arvind Bhatt Applied Science Department (Mathematics) Bipin trpathi Kumaun institute
More informationOn Multivalued G-Monotone Ćirić and Reich Contraction Mappings
Filomat 31:11 (2017), 3285 3290 https://doi.org/10.2298/fil1711285a Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On Multivalued
More informationAvailable online at Adv. Fixed Point Theory, 7 (2017), No. 1, ISSN:
Available online at http://scik.org Adv. Fixed Point Theory, 7 (2017), No. 1, 144-154 ISSN: 1927-6303 FIXED POINT THEOREMS UNDER F-CONTRACTION IN ULTRAMETRIC SPACE GINISWAMY 1, JEYANTHI C. 2,, MAHESHWARI
More informationResearch Article Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010, Article ID 746045, 15 pages doi:10.1155/2010/746045 Research Article Common Fixed Points of Weakly Contractive and Strongly
More informationOn Some Ćirić Type Results in Partial b-metric Spaces
Filomat 3: 07), 3473 348 https://doi.org/0.98/fil7473d Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On Some Ćirić Type Results
More informationCOMPLETENESS AND THE CONTRACTION PRINCIPLE J. M. BORWEIN'
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 87. Number 2. February IW COMPLETENESS AND THE CONTRACTION PRINCIPLE J. M. BORWEIN' Abstract. We prove (something more general than) the result that
More informationCommon Fixed Point Results in Complex Valued Metric Spaces with (E.A) and (CLR) Properties
Advances in Analysis, Vol., No. 4, October 017 https://dx.doi.org/10.606/aan.017.400 47 Common Fixed Point Results in Complex Valued Metric Spaces with (E.A) (CLR) Properties Mian Bahadur Zada 1, Muhammad
More informationFIXED POINTS OF MULTIVALUED MAPPING SATISFYING CIRIC TYPE CONTRACTIVE CONDITIONS IN G-METRIC SPACES
Hacettepe Journal of Mathematics and Statistics Volume 4() (03), 9 FIXED POINTS OF MULTIVALUED MAPPING SATISFYING CIRIC TYPE CONTRACTIVE CONDITIONS IN G-METRIC SPACES Mujahid Abbas, Talat Nazır and B.
More informationarxiv: v1 [math.fa] 8 Feb 2011
Compact Asymptotic Center and Common Fixed Point in Strictly Convex Banach Spaces arxiv:1102.1510v1 [math.fa] 8 Feb 2011 Ali Abkar and Mohammad Eslamian Department of Mathematics, Imam Khomeini International
More informationScalar Asymptotic Contractivity and Fixed Points for Nonexpansive Mappings on Unbounded Sets
Scalar Asymptotic Contractivity and Fixed Points for Nonexpansive Mappings on Unbounded Sets George Isac Department of Mathematics Royal Military College of Canada, STN Forces Kingston, Ontario, Canada
More informationA Fixed Point Theorem for Two Pair of Maps Satisfying a New Contractive Condition of Integral Type
International Mathematical Forum, 4, 29, no. 4, 177-183 A Fixed Point Theorem for Two Pair of Maps Satisfying a New Contractive Condition of Integral Type U. C. Gairola and A. S. Rawat Department of Mathematics
More informationCommon fixed points for α-ψ-ϕ-contractions in generalized metric spaces
Nonlinear Analysis: Modelling and Control, 214, Vol. 19, No. 1, 43 54 43 Common fixed points for α-ψ-ϕ-contractions in generalized metric spaces Vincenzo La Rosa, Pasquale Vetro Università degli Studi
More informationSOLUTION OF AN INITIAL-VALUE PROBLEM FOR PARABOLIC EQUATIONS VIA MONOTONE OPERATOR METHODS
Electronic Journal of Differential Equations, Vol. 214 (214), No. 225, pp. 1 1. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SOLUTION OF AN INITIAL-VALUE
More informationSOME NEW FIXED POINT RESULTS IN ULTRA METRIC SPACE
TWMS J. Pure Appl. Math., V.8, N.1, 2017, pp.33-42 SOME NEW FIXED POINT RESULTS IN ULTRA METRIC SPACE LJILJANA GAJIC 1, MUHAMMAD ARSHAD 2, SAMI ULLAH KHAN 3, LATIF UR RAHMAN 2 Abstract. The purpose of
More informationFIXED POINT RESULTS IN SELF MAPPING FUNCTIONS
Int. J. Engg. Res. & Sci. & Tech. 2016 M Ramana Reddy, 2016 Research Paper ISSN 2319-5991 www.ijerst.com Vol. 5, No. 4, November 2016 2016 IJERST. All Rights Reserved FIXED POINT RESULTS IN SELF MAPPING
More informationViscosity Iterative Approximating the Common Fixed Points of Non-expansive Semigroups in Banach Spaces
Viscosity Iterative Approximating the Common Fixed Points of Non-expansive Semigroups in Banach Spaces YUAN-HENG WANG Zhejiang Normal University Department of Mathematics Yingbing Road 688, 321004 Jinhua
More informationA GENERALIZATION OF CONTRACTION PRINCIPLE IN QUASI-METRIC SPACES
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 1(2017), Pages 92-108. A GENERALIZATION OF CONTRACTION PRINCIPLE IN QUASI-METRIC SPACES HAMZA
More informationIterative algorithms based on the hybrid steepest descent method for the split feasibility problem
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (206), 424 4225 Research Article Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem Jong Soo
More informationMULTIVALUED FIXED POINT RESULTS AND STABILITY OF FIXED POINT SETS IN METRIC SPACES. Binayak S. Choudhury, Nikhilesh Metiya, T. Som, C.
FACTA UNIVERSITATIS (NIŠ) Ser.Math.Inform. Vol. 30 No 4 (015) 501 51 MULTIVALUED FIXED POINT RESULTS AND STABILITY OF FIXED POINT SETS IN METRIC SPACES Binayak S. Choudhury Nikhilesh Metiya T. Som C. Bandyopadhyay
More informationOn Convergence Theorem for Nonself I - Nonexpansive Mapping in Banach Spaces
Applied Mathematical Sciences, Vol. 1, 2007, no. 48, 2379-2383 On Convergence Theorem for Nonself I - Nonexpansive Mapping in Banach Spaces H. Kiziltunc and M. Ozdemir Ataturk University, Faculty of Arts
More informationCommon fixed point results for multi-valued mappings with some examples
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 787 798 Research Article Common fixed point results for multi-valued mappings with some examples Afrah Ahmad Noan Abdou Department of
More informationCHARACTERIZATION OF REFLEXIVE BANACH SPACES WITH NORMAL STRUCTURE
Mathematica Moravica Vol. 6 (2002), 97 102 CHARACTERIZATION OF REFLEXIVE BANACH SPACES WITH NORMAL STRUCTURE Milan R. Tasković Abstract. This paper presents a characterization of reflexive Banach spaces
More informationWeak and strong convergence of a scheme with errors for three nonexpansive mappings
Rostock. Math. Kolloq. 63, 25 35 (2008) Subject Classification (AMS) 47H09, 47H10 Daruni Boonchari, Satit Saejung Weak and strong convergence of a scheme with errors for three nonexpansive mappings ABSTRACT.
More information