On Fixed Point Results for Matkowski Type of Mappings in G-Metric Spaces
|
|
- Claire Clark
- 6 years ago
- Views:
Transcription
1 Filomat 29: , DOI /FIL G Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: On Fixed Point Results for Matowsi Type of Mappings in G-Metric Spaces Lj. Gajić a, M. Stojaović b a Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Serbia b Department of Mathematics, Faculty of Technical Sciences, University of Novi Sad, Serbia Abstract. The main result of this paper is a fixed point theorem for Matowsi type mapping with contractive iterate at a point in a class of G-metric spaces. Our result unifies, generalizes and complements some well nown results in metric and G-metric spaces. 1. Introduction and preliminaries In 1975 Matowsi introduced the following class of mappings: Definition 1.1. [9] Let T be a mapping on a metric space X, d. Then T is called a wea contraction if there exists a function γ from [0, to itself satisfying the following: i γ is nondecreasing, ii lim n γ n t = 0 for all t > 0, iii dtx, Ty γdx, y for all x, y X. In the same paper he proved the existence and uniqueness of a fixed point for such type of mappings. This result is significant because the concept of wea contraction of Matowsi type is independent of Meir- Keeler contraction [12], and it was generalized in different directions [10], [11], [17]. Matowsi generalized his own result proving a theorem of Segal- Guseman type [6]. Theorem 1.2. [10] Let X, d be a complete metric space, T : X X, α : [0, 5 [0, and γt = αt, t, t, 2t, 2t for t 0. Suppose that 1. α is nondecreasing with respect to each variable, 2. lim t t γt =, 3. lim t γ n t = 0, t 0, 2010 Mathematics Subject Classification. Primary 47H10 Keywords. wea contraction, fixed point, mapping with contractive iterate at a point, G-metric space Received: 20 August 2014; Accepted: 11 Novemvber 2014 Communicated by Dragana Cvetović-Ilić This wor is supported by Ministry of Science and Technological Development, Republic of Serbia addresses: gajic@dmi.uns.ac.rs Lj. Gajić, stojaovic@sbb.rs M. Stojaović
2 Lj. Gajić, M. Stojaović / Filomat 29: , for every x X, there exists a positive integer n = nx such that for all y X dt n x, T n y αdx, y, dx, T n x, dx, T n y, dt n x, y, dt n y, y then T has a unique fixed point a X and for each x X, lim T x = a. The aim of this paper is to show that this result is valid in a more general class of spaces. On S. Gähler introduced 2-metric spaces, but other authors proved that there is no relation between two distance functions and there is no easy relationship between results obtained in the two settings. B. C. Dhage introduced a new concept of the measure of nearness between three or more objects. But topological structure of so called D-metric spaces was incorrect. Finally, Z. Mustafa and B. Sims [13] introduced correct definition of a generalized metric space as follows. Definition 1.3. [13] Let X be a nonempty set, and let G : X X X R + be a function satisfying the following properties G1 Gx, y, z = 0 if x = y = z; G2 0 < Gx, x, y, for all x, y X, with x y; G3 Gx, x, y Gx, y, z, for all x, y, z X, with z y; G4 Gx, y, z = Gx, z, y = Gy, z, x =..., symmetry in all three variables; G5 Gx, y, z Gx, a, a + Ga, y, z, for all x, y, z, a X. Then function G is called a generalized metric, abbreviated G-metric on X, and the pair X, G is called a G-metric space. Clearly these properties are satisfied when Gx, y, z is the perimeter of the triangle in with vertices x, y and z. R 2, moreover taing a in the interior of the triangle shows that G5 is the best possible. Example 1.1[13] Let X, d be an ordinary metric space, then X, d defines G-metrics on X by G s x, y, z = dx, y + dy, z + dx, z, G m x, y, z = max { dx, y, dy, z, dx, z }. Example 1.2[13] Let X = {a, b}. Define G on X X X by Ga, a, a = Gb, b, b = 0, Ga, a, b = 1, Ga, b, b = 2, and extend G to X X X by using the symmetry in the variables. Then it is clear the X, G is a G-metric space. The following useful properties of a G-metric are readily derived from the axioms. Proposition 1.4. [13] Let X, G be a G-metric space, then for any x, y, z and a from X it follows that: 1. if Gx, y, z = 0, then x = y = z, 2. Gx, y, z Gx, x, y + Gx, x, z, 3. Gx, x, y 2Gy, y, x, 4. Gx, y, z Gx, a, z + Ga, y, z, 5. Gx, y, z 2 3 Gx, y, a + Gx, a, z + Ga, y, z, 6. Gx, y, z Gx, a, a + Gy, a, a + Gz, a, a.
3 Lj. Gajić, M. Stojaović / Filomat 29: , Definition 1.5. [13] Let X, G be a G-metric space, and let {x n } be a sequence of points of X. A point x X is said to be the limit of the sequence {x n } if lim Gx, x n, x m = 0, and one says that the sequence {x n } is G-convergent to x. n,m Proposition 1.6. [13] Let X, G be a G-metric space, then for a sequence {x n } X and a point x X the following are equivalent: 1. {x n } is G-convergent to x, 2. Gx n, x n, x 0 as n, 3. Gx n, x, x 0 as n. Definition 1.7. [13] Let X, G be a G-metric space, a sequence {x n } is called G-Cauchy if for every ɛ > 0, there is N N such that Gx n, x m, x l < ɛ, for all n, m, l N, that is, if Gx n, x m, x l 0 as n, m, l. Proposition 1.8. [13] In a G-metric space X, G, the following are equivalent: 1. the sequence {x n } is G-Cauchy, 2. for every ε > 0, there exists an n 0 N such that Gx n, x m, x m < ε, for all n, m n 0. A G-metric space X, G is G-complete or G is a complete G-metric, if every G-Cauchy sequence in X, G is G-convergent in X, G. Proposition 1.9. [13] Let X, G be a G-metric space, then the function Gx, y, z is jointly continuous in all three of its variables. Recently, Samet at all [15] and Jleli,Samet [7] observed that some fixed point theorems in context of G- metric space can be proved by simple transformation using related existing results in the setting of metric space. Namely, if the contraction condition of the fixed point theorem on G-metric space can be reduced to two variables, then one can construct an equivalent fixed point theorem in setting of usual metric space. This idea is not completely new, but it was not successfully used before see [14]. Very recently, Karapinar and Agarwal suggest new contraction conditions in G-metric space in a way that the techniques in [15], [7] are not applicable. In this approach [8], contraction conditions can not be expressed in two variables. So, in some cases, as it is noticed even in Jleli-Samet paper [7], when the contraction condition is of nonlinear type, this strategy cannot be always successfully used. This is exactly the case in our paper. For more fixed point results for mappings defined in G-metric spaces, we refer the reader to [1], [2], [3], [4] [5], [14]. Definition Let X be a nonempty set and a function δ : X X [0, satisfies the following properties: 1. δx, y = 0 if and only if x = y, 2. δx, y δx, z + δz, y for any points x, y, z X, Then the pair X, δ is called a quasi -metric space. The sequence {x n } X converges to x X, iff lim n δx n, x = lim n δx, x n = Main result Let α : [0, 5 [0, be a nondecreasing function with respect to each variable and let γt = αt, t, 2t, 3t, 3t for t 0. Following Matowsi [10], let Γ be the set of all functions γ : [0, [0, such that 1 lim γ n t = 0, t > 0; 2 lim t t γt =.
4 Lj. Gajić, M. Stojaović / Filomat 29: , Simple examples of the function γ Γ are: γt = q t, q 0, 1, γt = t 1+t, γt = ln1 + t, t [0,. Remar 2.1. It is obvious that γ is nondecreasing function and that consequences of the condition lim t γ n t = 0, t 0, are: a γt < t, t > 0; b γ0 = 0. Definition 2.2. If X, G be a G-metric space, T : X X, and for every x X, there exists a positive integer n = nx such that for all y X GT nx x, T nx x, T nx y αgx, x, y, Gx, x, T nx y, Gx, T nx x, T nx x, Gy, T nx x, T nx x, Gy, y, T nx y, 2.1 then we say that T is a wea contraction in X. Lemma 2.3. If X, G is a G-metric space and T : X X is a wea contraction in X, then for every x X, the orbit {T x} is bounded. Proof. For any x X and any integer s, 0 s < nx we define the sequence u x, s = u = G x, x, Tx nx+s, = 0, 1, 2,... and the number hx, s = h = max { Gx, x, T nx x, Gx, T nx x, T nx x, Gx, x, T s x }. The property 2 of the function γ, implies that there exists a c, c > h, such that t γt > h, t > c. It is easy to see that u 0 < c. Next, we show that u j < c for all j = 0, 1, 2,.... The assumption that there exists a positive integer j such that u j c, but u i < c for i < j will lead to contradiction. Under the last assumption, G T nx x, T nx x, T j 1nx+s x h + u j 1 < 2u j, G T j 1nx+s x, T j 1nx+s x, T jnx+s x 2u j 1 + u j < 3u j. Now, since α is nondecreasing with respect to each variable and the mapping T is a wea contraction, we get u j = G x, x, T jnx+s x G x, x, T nx x + G T nx x, T nx x, T jnx+s x h + αu j, u j, u j, 2u j, 3u j h + γu j. The inequality u j γu j h contradicts to the choice of c. Hence, u j < c for all j = 0, 1,.... It completes the proof that for any fixed x X, sup Gx, x, T x = M <, meaning that the orbit {T x} is bounded. Lemma 2.4. If X, G is a G-metric space and T : X X is a wea contraction in X, then for every x 0 X, the sequence x +1 = T nx x, = 0, 1,..., is a Cauchy sequence.
5 Proof. It is easy to see that Lj. Gajić, M. Stojaović / Filomat 29: , x +j = T nx +j nx x, for all, j N. Using the notation s 0 = nx +j nx, we get G x, x, x +j = G x, x, T s 0 x Putting we obtain = G T nx 1 x 1, T nx 1 x 1, T nx 1 T s 0 x 1. t s1 = max { Gx 1, x 1, T i x 1 : i {s 0, nx 1, s 0 + nx 1 } }, G T nx 1 x 1, T nx 1 x 1, T s 0 x 1 2ts1 + t s1 = 3t s1 and G T nx 1+s 0 x 1, T s 0 x 1, T s 0 x 1 ts1 + 2t s1 = 3t s1. The property that the mapping T is a wea contraction with respect to nondecreasing function α implies G x, x, T s 0 x αt s1, t s1, 2t s1, 3t s1, 3t s1 = γt s1. Repeating this procedure, one concludes that there exists an s j N, j = 1, 2,..., 1 such that The mapping γ is nondecreasing which yields G x j, x j, T s j x j γ Gx j 1, x j 1, T s j+1 x j 1. G x, x, x +j γ G x 0, x 0, T s x 0 γ M. Since γ Γ, we see that lim γ n M = 0. This is precisely the assertion of the lemma, that is, {x } is a Cauchy sequence. Theorem 2.5. If X, G is a complete G-metric space and T : X X is a wea contraction in X, then T has a unique fixed point a X, for every x X, lim T x = a and T na is continuous at a. Proof. By completeness of X, the Cauchy sequence {x } defined in the above lemma is convergent, i.e. lim x = a X. The proof falls naturally into six consecutive parts in which we prove that: 1. T na a = a, 2. a is a unique fixed point of T na, 3. Ta = a, 4. a is a unique fixed point of T, 5. for every x X, lim T x = a, 6. T na is continuous at a 1. Applying the same reasoning as in the last lemma, we can show that lim Gx, x, T na x = 0. It means that for every ε > 0 there exists a 1 ε N such that for 1 ε, Gx, x, T na x < 1 ε γε. 8
6 Lj. Gajić, M. Stojaović / Filomat 29: , Since lim Gx, x, a = 0, for every ε > 0 there exists a 2 ε N such that for 2 ε, Ga, x, x < 1 ε γε 8 Next, we claim that T na a = a. Indeed, if we suppose the opposite, i.e. if we suppose that there exists an ε > 0 such that GT na a, T na a, a = ε, then for max{ 1 ε, 2 ε} ε = GT na a, T na a, a GT na a, T na a, T na x The next two relations +GT na x, T na x, x + Gx, x, a α Ga, a, x, Ga, a, T na x, Ga, T na a, T na a, Gx, T na a, T na a, Gx, x, T na x + 1 ε γε. 2 Ga, a, T na x Ga, a, x + Gx, x, T na x < 1 ε γε, 4 imply Gx, T na a, T na a Gx, a, a + Ga, T na a, T na a < 2ε, ε αε, ε, ε, 2ε, ε ε γε < 1 ε + γε < ε, 2 which is a contradiction, meaning that the assumption that T na a a is not correct. 2. The proof that a is the only fixed point of the mapping T na is once again by contradiction. If b X would be another fixed point of T na, then Ga, a, b = GT na a, T na a, T na b αga, a, b, Ga, a, b, 0, Gb, a, a, 0 γga, a, b < Ga, a, b, which establishes our claim that a = b. 3. The equality T a = T T na a = T na T a implies that T a = a. 4. From 2. and 3. we conclude that a is the only point from X such that T a = a. 5. Next we prove that lim T x = a, for each x X. For each x X and each s N, 0 s < na, define the sequence a = Ga, a, T na+s x, = 0, 1, 2,. If for some N, a > a 1, then a = GT na a, T na a, T na T 1na+s x α G a, a, T 1na+s x, G a, a, T na+s x, G a, T na a, T na a, G T na+s x, T na a, T na a, G T 1na+s x, T 1na+s x, T na+s x αa 1, a, 0, a 1, a + 2a 1 γa < a. By the last contradiction, we deduce that a a 1 for all N. Hence, a αa 1, a 1, a 1, a 1, 3a 1 γa 1 γ a 0.
7 Lj. Gajić, M. Stojaović / Filomat 29: , Letting in the last relation, lim a = lim γ a 0 = 0, and consequently lim T x = a. 6. Finally, we finish the proof by showing the continuity of T na at a. We consider a sequence {y m } m X converging to a. For any m N G a, a, T na y m = GT na a, T na a, T na y m α G a, a, y m, G a, a, T na y m, G a, T na a, T na a, G y m, T na a, T na a, G y m, y m, T na y m = α G a, a, y m, G a, a, T na y m, G a, a, a, G y m, a, a, G y m, y m, T na y m α G a, a, y m, G a, a, T na y m, 0, G y m, a, a, G y m, y m, a + G a, a, T na y m. If lim m G a, a, T na y m 0, then there exists ε > 0 such that for some m1 N, G a, a, T na y m > ε for all m > m 1. On the other hand, since lim y m = a, for given ε there exist m 2 N and m 3 N such that and m > m 2 G a, a, y m < ε < G a, a, T na y m, m > m 3 G y m, y m, a < ε < G a, a, T na y m. Putting m 0 = max{m 1, m 2, m 3 }, for all m > m 0, we get G a, a, T na y m α G a, a, T na y m, G a, a, T na y m, 0, G a, a, T na y m, 2G a, a, T na y m γ G a, a, T na y m < G a, a, T na y m. Obviously, the assumption lim m G a, a, T na y m 0 induces the contradiction in the last relation. Hence, T na is continuous at a. Remar 2.6. In a symmetric G-metric space, one can put γt = αt, t, t, 2t, 2t as it is done in Matovsi paper [10], but Jleli-Samet technique can not be applied. In [7] it was shown that if X,G is a G-metric space, putting δx, y = Gx, y, y, X, δ is a quasi metric space δ is not symmetric. Simple replacement G with δ in 2.1, defines the wea contraction T in X, δ δt nx x, T nx y αδx, y, δx, T nx y, δt nx x, x, δt nx x, y, δy, T nx y. The following result is an immediate consequence of above definitions and relations. Theorem 2.7. If X, δ is a complete quasi-metric space such that δx, y 2δy, x for all x, y X and T : X X is a wea contraction in X, then T has a unique fixed point a X, for every x X, lim T x = a and T na is continuous at a. Proof. It is obvious that X, δ has the same topological structure as any G-metric space X, G where G satisfies equality δx, y = Gx, y, y. Now, repeating the proof of Theorem 2.5, we conclude that the assertion of theorem is true.
8 Lj. Gajić, M. Stojaović / Filomat 29: , The next few corollaries are also a consequence of Theorem 2.5. Corollary 2.8. [5] Let X, G be a complete G-metric space, T : X X, γ Γ and for each x X there exists a positive integer n = nx such that G T nx x, T nx x, T nx y γ Gx, x, y, 2.2 for all y X. Then T has a unique fixed point a X. Moreover, for each x X, lim at a. T x = a and T na is continuous Corollary 2.9. [3] Let X, G be a complete G-metric space, T : X X and for each x X there exists a positive integer n = nx such that G T nx x, T nx x, T nx y q Gx, x, y for all y X and some q 0, 1. Then T has a unique fixed point a X. Moreover, for each x X, lim T na is continuous at a. T x = a and Proof. Function γt = q t, t [0,, belongs to Γ, so corollary is a consequence of Theorem 2.5. Remar Taing γt = q t, 0 < q < 1, we obtain the fixed point result from [2] or [3], so Theorem 2.5. is also a generalization of Guseman fixed point result from [6]. Corollary Let X, G be a complete G-metric space, T : X X, and for each x X there exists a positive integer n = nx such that G T nx x, T nx x, T nx y Gx, x, y 1 + Gx, x, y, for all y X. Then T has a unique fixed point a X. Moreover, for each x X, lim at a. Proof. Since the function γ = T x = a and T na is continuous t 1+t, t [0,, belongs to the family Γ, we can apply Theorem 2.5. If nx = 1 nx = m N, for each x X, we are going to prove that condition 3 can be omitted so, in that case we will have an improvement and another proof of Theorem 3.1 Corollary 3.2 from [16]. Proposition Let X, G be a complete G-metric space, γ : [0, [0, be a nondecreasing function with lim γ t = 0 for t > 0. If T : X X satisfies G Tx, Tx, Ty γgx, x, y, for all x, y X, then T has a unique fixed point a X. Moreover, for each x X, lim at a. 2.3 T x = a and T na is continuous Proof. We prove, by induction, that for any x 0 = x, x X, the orbit {T x 0 } is bounded. By the properties of the function γ, lim γ Gx 0, x 0, x 1 = 0 and γt < t, t > 0, we get that there exists 0 N such that for all 0 Hence γ Gx 0, x 0, x 1 < 1 γ1. G Tx, Tx, Tx +1 < 1 γ1, For j > 0, j N, we claim that G x 0, x 0, x j
9 Lj. Gajić, M. Stojaović / Filomat 29: , Indeed, for j = 0 + 1, the last relation is true by 2.4. Assuming inequality 2.5 holds for j = i, i > 0, we will prove it holds for j = i + 1. Really, letting j = i + 1, we get G x 0, x 0, x i+1 G x0, x 0, x G x0 +1, x 0 +1, x i+1 Finally, for any N G x 0, x 0, x γ G x0, x 0, x i 1 γ1 + γ1 = 1. G x 0, x 0, T x 0 G x0, x 0, x 0 + G x0, x 0, x G x 0, x 0, x 0 + max{1, G x0, x 0, x 1,, G x0, x 0, x 0 1 = M <. Now, the rest of the proof runs as in Theorem 2.1. References [1] M. Abbas, B.E. Rhoades, Common fixed point results for noncommuting mapping without continuity in generalized metric space, Applied Mathematics and Computation, [2] Lj. Gajić, Z. Lozanov-Crvenović, On mappings with contractive iterate at a point in generalized metric spaces, Fixed Point Theory and Applications. 2010, Article ID , 16 pages, doi: /2010/ [3] LJ. Gajić, Z. Lozanov-Crvenović, A fixed point result for mappings with contractive iterate at a point in G-metric spaces, Filomat, [4] LJ. Gajić, M. Stojaović, On Ćirić generalization of mappings with a contractive iterate at a point in G-metric space, Applied Mathematics and Computation, [5] LJ. Gajić, M. Stojaović, On mappings with ϕ-contractive iterate at a point on generalized metric spaces, Fixed Point Theory and Applications 2014, 2014:46 [6] L. F. Guseman, Fixed point theorems for mappings with a contractive iterate at a point, Proceedings of American Mathematical Society, [7] M. Jleli, B. Samet, Remars on G-metric spaces and fixed point theorems, Fixed Point Theory and Applications, 2012, 2012:210, doi: / [8] E. Karapinar, R. Agarval, Further remars on G-metric spaces, Fixed Point Theory and Applications 2013, 2013:154 doi: / [9] J. Matowsi, Integrable solutions of functional equations, Dis.Math., 127, Warsaw, [10] J. Matowsi, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., [11] J. Matowsi, Fixed point theorems for contractive mappings in metric spaces, Casopis Pest. Mat., [12] A. Meir, E. Keeler, A theorem on contraction mappings, Journal of Mathematical Analysis and Application, [13] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear Convex Analysis, [14] Z. Mustafa, H. Obiedat, H. Awawdeh, Some fixed point theorem for mappings on complete G-metric spaces, Fixed Point Theory and Applications 2008 article ID ,12 pages. [15] B. Samet, C. Vetro, F. Vetro, Remars on G-Metric Spaces, International Journal of Analysis, Volume , Article ID , 6 pages [16] W. Shatanawi, Fixed Point Theory for Contractive Mappings Satisfying Φ-Maps in G-Metric Spaces, Fixed Point Theor. Appl Article ID , 9 pages. [17] T. Suzui, C. Vetro, Three existence theorems for wea contraction of Matowsi type, International Journal of Mathematical Statistics, ISSN:
Research Article On Mappings with Contractive Iterate at a Point in Generalized Metric Spaces
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010, Article ID 458086, 16 pages doi:10.1155/2010/458086 Research Article On Mappings with Contractive Iterate at a Point in Generalized
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 informationSome Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces
Mathematica Moravica Vol. 17-1 (013) 5 37 Some Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces Amit Singh B. Fisher and R.C. Dimri Abstract. In this paper we prove some fixed point
More informationG p -metric spaces symmetric and asymmetric
SCIENTIFIC PUBLICATIONS OF THE STATE UNIVERSITY OF NOVI PAZAR SER. A: APPL. MATH. INFORM. AND MECH. vol. 9, 1 (2017), 37-46. G p -metric spaces symmetric and asymmetric Ljiljana Gajić, Zoran Kadelburg,
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 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 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 informationSome new fixed point theorems in metric spaces
Mathematica Moravica Vol. 20:2 (206), 09 2 Some new fixed point theorems in metric spaces Tran Van An and Le Thanh Quan Abstract. In this paper, the main results of [3] are generalized. Also, examples
More informationV. Popa, A.-M. Patriciu ( Vasile Alecsandri Univ. Bacău, Romania)
UDC 51791 V Popa, A-M Patriciu ( Vasile Alecsandri Univ Bacău, Romania) FIXED-POINT RESULTS ON COMPLETE G-METRIC SPACES FOR MAPPINGS SATISFYING AN IMPLICIT RELATION OF A NEW TYPE РЕЗУЛЬТАТИ ПРО НЕРУХОМУ
More informationBEST PROXIMITY POINT RESULTS VIA SIMULATION FUNCTIONS IN METRIC-LIKE SPACES
Kragujevac Journal of Mathematics Volume 44(3) (2020), Pages 401 413. BEST PROXIMITY POINT RESULTS VIA SIMULATION FUNCTIONS IN METRIC-LIKE SPACES G. V. V. J. RAO 1, H. K. NASHINE 2, AND Z. KADELBURG 3
More informationS. K. Mohanta, Srikanta Mohanta SOME FIXED POINT RESULTS FOR MAPPINGS IN G-METRIC SPACES
DEMONSTRATIO MATHEMATICA Vol. XLVII No 1 2014 S. K. Mohanta Srikanta Mohanta SOME FIXED POINT RESULTS FOR MAPPINGS IN G-METRIC SPACES Abstract. We prove a common fixed point theorem for a pair of self
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 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 informationNonexpansive Mappings in the Framework of Ordered S-Metric Spaces and Their Fixed Points
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-349, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
More informationInvariant Approximation Results of Generalized Contractive Mappings
Filomat 30:14 (016), 3875 3883 DOI 10.98/FIL1614875C Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Invariant Approximation Results
More informationCOUPLED FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
Kragujevac Journal of Mathematics Volume 382 2014, Pages 249 257. COUPLED FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES STOJAN RADENOVIĆ Abstract. In this paper, by reducing
More informationSome 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 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 informationSome fixed point theorems in G-metric spaces
Math. Sci. Lett. 1, No. 1, 25-31 (2012) 25 Mathematical Sciences Letters. An International Journal Some fixed point theorems in G-metric spaces Binayak S 1. Choudhury 1, Sanjay Kumar 2, Asha 3 and Krishnapada
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 informationFixed Point Theorem of Ćirić Type in Weak Partial Metric Spaces
Filomat 31:11 017), 303 307 https://doi.org/10.98/fil171103p Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Theorem
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 informationFixed Points for Multivalued Mappings in b-metric Spaces
Applied Mathematical Sciences, Vol. 10, 2016, no. 59, 2927-2944 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.68225 Fixed Points for Multivalued Mappings in b-metric Spaces Seong-Hoon
More informationSPACES ENDOWED WITH A GRAPH AND APPLICATIONS. Mina Dinarvand. 1. Introduction
MATEMATIČKI VESNIK MATEMATIQKI VESNIK 69, 1 (2017), 23 38 March 2017 research paper originalni nauqni rad FIXED POINT RESULTS FOR (ϕ, ψ)-contractions IN METRIC SPACES ENDOWED WITH A GRAPH AND APPLICATIONS
More informationSOME FIXED POINT RESULTS FOR ADMISSIBLE GERAGHTY CONTRACTION TYPE MAPPINGS IN FUZZY METRIC SPACES
Iranian Journal of Fuzzy Systems Vol. 4, No. 3, 207 pp. 6-77 6 SOME FIXED POINT RESULTS FOR ADMISSIBLE GERAGHTY CONTRACTION TYPE MAPPINGS IN FUZZY METRIC SPACES M. DINARVAND Abstract. In this paper, we
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 informationDouble Contraction in S-Metric Spaces
International Journal of Mathematical Analysis Vol. 9, 2015, no. 3, 117-125 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.1135 Double Contraction in S-Metric Spaces J. Mojaradi Afra
More informationCommon fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces
Tahat et al Fixed Point Theory and Applications 202 202:48 http://wwwfixedpointtheoryandapplicationscom/content/202//48 RESEARCH Open Access Common fixed points for single-valued and multi-valued maps
More informationNew extension of some fixed point results in complete metric spaces
DOI 10.1515/tmj-017-0037 New extension of some fixed point results in complete metric spaces Pradip Debnath 1,, Murchana Neog and Stojan Radenović 3 1, Department of Mathematics, North Eastern Regional
More informationNEW TYPE OF RESULTS INVOLVING CLOSED BALL WITH GRAPHIC CONTRACTION
Journal of Inequalities and Special Functions ISSN: 17-4303 URL: http://ilirias.com/jiasf Volume 7 Issue 4(016) Pages 36-48. NEW TYPE OF RESULTS INVOLVING CLOSED BALL WITH GRAPHIC CONTRACTION AFTAB HUSSAINMUHAMMAD
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 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 informationA FIXED POINT THEOREM FOR UNIFORMLY LOCALLY CONTRACTIVE MAPPINGS IN A C-CHAINABLE CONE RECTANGULAR METRIC SPACE
Surveys in Mathematics and its Applications A FIXED POINT THEOREM FOR UNIFORMLY LOCALLY CONTRACTIVE MAPPINGS IN A C-CHAINABLE CONE RECTANGULAR METRIC SPACE Bessem Samet and Calogero Vetro Abstract. Recently,
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 informationCHAPTER 1. Metric Spaces. 1. Definition and examples
CHAPTER Metric Spaces. Definition and examples Metric spaces generalize and clarify the notion of distance in the real line. The definitions will provide us with a useful tool for more general applications
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 informationA fixed point problem under two constraint inequalities
Jleli and Samet Fixed Point Theory and Applications 2016) 2016:18 DOI 10.1186/s13663-016-0504-9 RESEARCH Open Access A fixed point problem under two constraint inequalities Mohamed Jleli and Bessem Samet*
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 informationOn Measure of Non-Compactness in Convex Metric Spaces. Ljiljana Gajić
Faculty of Sciences and Mathematics University of Niš Available at: www.pmf.ni.ac.yu/org/filomat/welcome.htm Filomat 19 (2005), 1 5 On Measure of Non-Compactness in Convex Metric Spaces Ljiljana Gajić
More informationA Fixed Point Theorem of Reich in G-Metric Spaces
CUBO A Mathematical Journal Vol.12, N ō 01, (83 93). March 2010 A Fixed Point Theorem of Reich in G-Metric Spaces Zead Mustafa and Hamed Obiedat The Hashemite University, Department of Mathematics, P.O.
More informationFIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES. 1. Introduction and preliminaries
Asia Pacific Journal of Mathematics, Vol. 1, No. 1 (2014), 67-85 ISSN 2357-2205 FIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES ANIMESH GUPTA Department of Applied Mathematics, Vidhyapeeth
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 informationA Fixed Point Theorem for G-Monotone Multivalued Mapping with Application to Nonlinear Integral Equations
Filomat 31:7 (217), 245 252 DOI 1.2298/FIL17745K Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Fixed Point Theorem for G-Monotone
More informationFixed Point Theorems for Contractions and Generalized Contractions in Compact G-Metric Spaces
Journal of Interpolation and Approximation in Scientific Computing 2015 No.1 (2015) 20-27 Available online at www.ispacs.com/jiasc Volume 2015, Issue 1, Year 2015 Article ID jiasc-00071, 8 Pages doi:10.5899/2015/jiasc-00071
More informationCoincidence point results of multivalued weak C-contractions on metric spaces with a partial order
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 6 (2013), 7 17 Research Article Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order Binayak S. Choudhury
More informationThe (CLR g )-property for coincidence point theorems and Fredholm integral equations in modular metric spaces
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 1, No., 17, 38-54 ISSN 137-5543 www.ejpam.com Published by New York Business Global The (CLR g )-property for coincidence point theorems and Fredholm
More informationA Fixed Point Theorem for JS-contraction Type Mappings with Applications to Polynomial Approximations
Filomat 31:15 (2017, 4969 4978 https://doi.org/10.2298/fil1715969a Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Fixed Point
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 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 informationCOMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS WITH SOME WEAK CONDITIONS OF COMMUTATIVITY
Novi Sad J. Math. Vol. 36, No. 1, 006, 75-86 COMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS WITH SOME WEAK CONDITIONS OF COMMUTATIVITY Duran Turkoglu 1, Ishak Altun 1, Brian Fisher Abstract. Some results
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 informationA generalization of Banach s contraction principle for nonlinear contraction in a partial metric space
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 5 (01), 37 43 Research Article A generalization of Banach s contraction principle for nonlinear contraction in a partial metric space Wasfi Shatanawi
More informationA Fixed Point Theorem For Multivalued Maps In Symmetric Spaces
Applied Mathematics E-Notes, 4(2004), 26-32 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ A Fixed Point Theorem For Multivalued Maps In Symmetric Spaces Driss El
More informationQuadruple Coincidence Point Results in Partially Ordered Metric Spaces
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN p 2303-367 ISSN o 2303-955 wwwimviblorg / JOURNALS / BULLETIN OF IMVI Vol 201 5-52 doi: 117251/BIMVI10105G Former BULLETIN OF SOCIETY OF
More informationAvailable online at Advances in Fixed Point Theory, 2 (2012), No. 1, ISSN:
Available online at http://scik.org Advances in Fixed Point Theory, 2 (2012), No. 1, 29-46 ISSN: 1927-6303 COUPLED FIXED POINT RESULTS UNDER TVS-CONE METRIC AND W-CONE-DISTANCE ZORAN KADELBURG 1,, STOJAN
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 informationCoupled Fixed Point Theorems for Nonlinear Contractions in G-Metric Spaces
Sohag J. Math. 1, No. 1, 1-5 (2014) 1 Sohag Journal of Mathematics An International Journal http://dx.doi.org/10.12785/sjm/010101 Coupled Fixed Point Theorems for Nonlinear Contractions in G-Metric Spaces
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 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 informationA fixed point theorem for Meir-Keeler contractions in ordered metric spaces
RESEARCH Open Access A fixed point theorem for Meir-Keeler contractions in ordered metric spaces Jackie Harjani, Belén López and Kishin Sadarangani * * Correspondence: ksadaran@dma. ulpgc.es Departamento
More informationCOUPLED FIXED AND COINCIDENCE POINT THEOREMS FOR GENERALIZED CONTRACTIONS IN METRIC SPACES WITH A PARTIAL ORDER
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 39 2018 (434 450) 434 COUPLED FIXED AND COINCIDENCE POINT THEOREMS FOR GENERALIZED CONTRACTIONS IN METRIC SPACES WITH A PARTIAL ORDER K. Ravibabu Department
More informationBest proximity points for generalized α η ψ-geraghty proximal contraction mappings
Mathematica Moravica Vol. 1, No. (017), 85 10 Best proximity points for generalized α η ψ-geraghty proximal contraction mappings K.K.M. Sarma and Yohannes Gebru Abstract. In this paper, we introduce the
More informationFixed point results and an application to homotopy in modular metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 8 (015), 900 908 Research Article Fixed point results and an application to homotopy in modular metric spaces Meltem Erden Ege a, Cihangir Alaca
More informationOn Best Proximity Point Theorems for New Cyclic Maps
International Mathematical Forum, Vol. 7, 2012, no. 37, 1839-1849 On Best Proximity Point Theorems for New Cyclic Maps Ing-Jer Lin 1, Hossein Lakzian 2 and Yi Chou 1 1 Department of Mathematics National
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 informationComparison of the Rate of Convergence of Various Iterative Methods for the Class of Weak Contractions in Banach Spaces
Thai Journal of Mathematics Volume 11 (2013) Number 11 : 217 226 http://thaijmathincmuacth ISSN 1686-0209 Comparison of the Rate of Convergence of Various Iterative Methods for the Class of Weak Contractions
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 informationCommon fixed points for a class of multi-valued mappings and application to functional equations arising in dynamic programming
Malaya J. Mat. 2(1)(2014) 82 90 Common fixed points for a class of multi-valued mappings and application to functional equations arising in dynamic programming A. Aghajani, a E. Pourhadi b, a,b School
More informationA fixed point theorem on soft G-metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 885 894 Research Article A fixed point theorem on soft G-metric spaces Aysegul Caksu Guler a,, Esra Dalan Yildirim b, Oya Bedre Ozbakir
More informationTools from Lebesgue integration
Tools from Lebesgue integration E.P. van den Ban Fall 2005 Introduction In these notes we describe some of the basic tools from the theory of Lebesgue integration. Definitions and results will be given
More informationNew Nonlinear Conditions for Approximate Sequences and New Best Proximity Point Theorems
Applied Mathematical Sciences, Vol., 207, no. 49, 2447-2457 HIKARI Ltd, www.m-hikari.com https://doi.org/0.2988/ams.207.7928 New Nonlinear Conditions for Approximate Sequences and New Best Proximity Point
More informationSome Generalizations of Caristi s Fixed Point Theorem with Applications
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 12, 557-564 Some Generalizations of Caristi s Fixed Point Theorem with Applications Seong-Hoon Cho Department of Mathematics Hanseo University, Seosan
More informationMath 421, Homework #9 Solutions
Math 41, Homework #9 Solutions (1) (a) A set E R n is said to be path connected if for any pair of points x E and y E there exists a continuous function γ : [0, 1] R n satisfying γ(0) = x, γ(1) = y, and
More informationResearch Article Generalized α-ψ Contractive Type Mappings and Related Fixed Point Theorems with Applications
Abstract and Applied Analysis Volume 01, Article ID 793486, 17 pages doi:10.1155/01/793486 Research Article Generalized α-ψ Contractive Type Mappings and Related Fixed Point Theorems with Applications
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 informationApplication of Measure of Noncompactness for the System of Functional Integral Equations
Filomat 3:11 (216), 363 373 DOI 1.2298/FIL161163A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Application of Measure of Noncompactness
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 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 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 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 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 informationFixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces
RESEARCH Open Access Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces Ljubomir Ćirić 1*, Hossein Lakzian 2 and Vladimir Rakočević 3 * Correspondence: lciric@rcub.bg.
More informationProperty Q and a Common Fixed Point Theorem of (ψ, ϕ)-weakly Contractive Maps in G-Metric Spaces
J. Ana. Num. Theor. 1, No. 1, 23-32 (2013) 23 Journal of Analysis & Number Theory An International Journal Property Q and a Common Fixed Point Theorem of (ψ, ϕ)-weakly Contractive Maps in G-Metric Spaces
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 informationCourse 212: Academic Year Section 1: Metric Spaces
Course 212: Academic Year 1991-2 Section 1: Metric Spaces D. R. Wilkins Contents 1 Metric Spaces 3 1.1 Distance Functions and Metric Spaces............. 3 1.2 Convergence and Continuity in Metric Spaces.........
More informationFIXED POINT OF α-geraghty CONTRACTION WITH APPLICATIONS
U.P.B. Sci. Bull., Series A, Vol. 78, Iss., 016 ISSN 13-707 FIXED POINT OF α-geraghty CONTRACTION WITH APPLICATIONS Muhammad Arshad 1, Aftab Hussain, Akbar Azam 3 Cho, Bae and Karapinar [Fixed point theorems
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 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 informationFixed Point Theorems for Generalized β φ contractive Pair of Mappings Using Simulation Functions
Bol. Soc. Paran. Mat. (3s.) v. 00 0 (0000):????. c SPM ISSN-175-1188 on line ISSN-0037871 in press SPM: www.spm.uem.br/bspm doi:10.569/bspm.40870 Fixed Point Theorems for Generalized β φ contractive Pair
More informationCommon Fixed Point Theorems for Multivalued β -ψ-contractive Mappings
Thai Journal of Mathematics Volume 15 (2017) Number 3 : 747 759 http://thaijmath.in.cmu.ac.th ISSN 1686-0209 Common Fixed Point Theorems for Multivalued β -ψ-contractive Mappings Tanusri Senapati and Lakshmi
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 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 informationSome Common Fixed Point Theorems on G-Metric Space
Gen. Math. Notes, Vol. 1, No., April 014, pp.114-14 ISSN 19-7184; Copyright c ICSRS Publication, 014 www.i-csrs.org Available free online at http://www.geman.in Some Common Fixed Point Theorems on G-Metric
More informationFixed points of almost quadratic Geraghty contractions and property(p) in partially ordered metric spaces
Journal of Advanced Research in Applied Mathematics Online ISSN: 1942-9649 Vol. 7, Issue., 2015, pp. 1-9 doi: 10.5373/jaram. 1 2 3 4 5 6 7 Fixed points of almost quadratic Geraghty contractions and property(p)
More informationDiscussion on the fixed point problems with constraint inequalities
Alqahtani et al. Journal of Inequalities and Applications (018) 018:4 https://doi.org/10.1186/s13660-018-1818-4 R E S E A R C H Open Access Discussion on the fixed point problems with constraint inequalities
More informationCommon fixed points for maps on cone metric space
J. Math. Anal. Appl. 341 (2008) 876 882 www.elsevier.com/locate/jmaa Common fixed points for maps on cone metric space Dejan Ilić, Vladimir Rakočević University of Niš, Faculty of Sciences and Mathematics,
More informationCommon fixed point theorems on non-complete partial metric spaces
466 Nonlinear Analysis: Modelling and Control, 2013, Vol. 18, No. 4, 466 475 Common fixed point theorems on non-complete partial metric spaces Shaban Sedghi a, Nabi Shobkolaei b, Ishak Altun c a Department
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 informationKannan Fixed-Point Theorem On Complete Metric Spaces And On Generalized Metric Spaces Depended an Another Function
arxiv:0903.1577v1 [math.fa] 9 Mar 2009 Kannan Fixed-Point Theorem On Complete Metric Spaces And On Generalized Metric Spaces Depended an Another Function S. Moradi Faculty of Science, Department of Mathematics
More informationSOME FIXED POINT THEOREMS IN EXTENDED b-metric SPACES
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018 ISSN 1223-7027 SOME FIXED POINT THEOREMS IN EXTENDED b-metric SPACES Wasfi Shatanawi 1, Kamaleldin Abodayeh 2, Aiman Mukheimer 3 In this paper, we introduce
More information