Ciric-type δ-contractions in metric spaces endowedwithagraph
|
|
- Ruby Blankenship
- 5 years ago
- Views:
Transcription
1 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 R E S E A R C H Open Access Ciric-type δ-contractions in metric spaces endowedwithagraph Cristian Chifu 1* and Adrian Petruşel 2 * Correspondence: cristian.chifu@tbs.ubbcluj.ro 1 Department of Business, Babeş-Bolyai University Cluj-Napoca, Horea street, 7, Cluj-Napoca, , Romania Full list of author information is available at the end of the article Abstract The purpose of this paper is to present some fixed-point and strict fixed-point results in a metric space endowed with a graph, using a contractive condition of Ćirić type with respect to the functional δ. The data dependence of the fixed-point set, the well-posedness of the fixed-point problem, and the limit shadowing property are also studied. MSC: 47H10; 54H25 Keywords: fixed point; strict fixed point; metric space; connected graph; well-posed problem; limit shadowing property 1 Preliminaries A recent research direction in fixed-point theory is the study of the fixed-point problem for single-valued and multivalued operators in the context of a metric space endowed with a graph. This approach was recently considered by Jachymski in [1], Gwóźdź-Lukawska and Jachymski in [2],andthenitwasdevelopedinmanyotherpapers[3 5], etc.. On the other hand, fixed points and strict fixed points also called end-points are important elements in mathematical economics and game theory. It represents optimal preferencesinsomearrow-debreutypemodelsornashtypeequilibriumpointsforsome abstract noncooperative games, see, for example, [6] and[7]. From this perspective, it is important to give fixed and strict fixed-point theorems for multivalued operators. We shall begin by presenting some notions and notations that will be used throughout the paper. Let X, d be a metric space and be the diagonal of X X. LetG be a directed graph such that the set V G of its vertices coincides with X and EG, EGbeingthesetof the edges of the graph. Assuming that G has no parallel edges, we will suppose that G can be identified with the pair V G, EG. If x and y are vertices of G,thenapathinG from x to y of length k N is a finite sequence x n n {0,1,2,...,k} of vertices such that x 0 = x, x k = y and x i 1, x i EG, for i {1,2,...,k}. Let us denote by G the undirected graph obtained from G by ignoring the direction of edges. Notice that a graph G is connected if there is a path between any two vertices and it is weakly connected if G is connected. Let us consider the following families of subsets of a metric space X, d: PX:= { Y PX Y }, P b X:= { Y PX Y is bounded }, P cl X:= { Y PX Y is closed }, P cp X:= { Y PX Y is compact } Chifu and Petruşel; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
2 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 2 of 11 Let usdefine thegap functionalbetween the sets A and B in the metric space X, d as: D : PX PX R + {+ }, DA, B=inf { da, b a A, b B } and the generalized Pompeiu-Hausdorff functional as H : PX PX R + {+ }, { HA, B=max sup a A Da, B, sup DA, b b B }. The generalized diameter functional is denoted by δ : PX PX R + { },and defined by δa, B=sup { da, b a A, b B }. Denote by diama:=δa, A the diameter of the set A. Let T : X PX beamultivaluedoperatorandgraphict :={x, y y Tx} the graphic of T. x X is called fixed point for T if and only if x Tx, and it is called strict fixed point if and only if {x} = Tx. The set FixT :={x X x Tx} is called the fixed-point set of T, whiles FixT = {x X {x} = Tx} is called the strict fixed-point set of T.NoticethatS FixT FixT. We will write EG IT Tifandonlyifforeveryx, y X with x, y EGwehave Tx Ty EG. For the particular case of a single-valued operator t : X X the above notations should be considered accordingly. In particular, the condition EG It t means that the operator t is edge preserving in the sense of the Jachymski s definition of a Banach contraction, i.e. for each x, y X with x, y EG we havetx,ty EG see[1]. We will also denote by Ox 0, n:={x 0, tx 0, t 2 x 0,...,t n x 0 } the orbit of order n of the operator t corresponding to x 0 X. In this paper we prove some fixed-point and strict fixed-point theorems for singlevalued and multivalued operators satisfying a contractive condition of Ćirić type with respect to the functional δ. Our results also generalize and extend some fixed-point theorems in partially ordered complete metric spaces given in Harjani, Sadarangani [8],Nieto, Rodríguez-López [9] and[10], Nieto et al. [11], O Regan, Petruşel [12], Petruşel, Rus [13] and Ran, Reurings [14]. For other general results concerning Ćirić type fixed-point theorems see Rus [15]. In the main section of the paper we give results concerning the existence and uniqueness of the fixed point and of the strict fixed point of a Ćirić type single-valued and multivalued contraction. Then the well-posedness of the fixed-point problem, the data dependence of the fixed-point set, and the limit shadowing property are also studied. Our results complement and extend some recent theorems given in [16] for multivalued Reich-type operators. 2 Main results In this section we present the main results of the paper concerning the fixed-point problem and, respectively, the strict fixed-point problem for a single-valued, respectively, of a multivalued Ćirić type contraction.
3 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 3 of 11 Definition 2.1 Let X, dbeametricspaceandt : X P cl Xbeamultivaluedoperator. By definition, the fixed-point problem is well-posed for T with respect to H if: i S Fix T = {x }; d ii If x n n N is a sequence in X such that Hx n, Tx n 0,asn,thenx n x, as n. Definition 2.2 Let X, d be a metric space and T : X PX beamultivaluedoperator. By definition T has the limit shadowing property if for any sequence y n n N from X such that Dy n+1, Ty n 0, as n,thereexistsx n n N, a sequence of successive approximation of T,suchthatdx n, y n 0, as n. In order to prove the limit shadowing property we shall need Cauchy s lemma. Lemma 2.1 Cauchy s lemma Let a n n N and b n n N be two sequences of non-negative real numbers, such that + k=0 a k <+ and b n 0, as n. Then n a n k b k 0, k=0 as n. The first main result of this paper is the following result for the case of single-valued operators. The proof of this result is inspired by the proof of Ćirić s fixed-point theorem in [17] and the approach introduced for metric spaces endowed with a graph by Jachymski in [1]. Theorem 2.1 Let X, d be a complete metric space and G be a directed graph such that the triple X, d, G satisfies the following property: P for any sequence x n n N Xwithx n xasn, there exists a subsequence x kn n N of x n n N such that x kn, x EG. Let t : X Xbeasingle-valuedoperator. Suppose the following assertions hold: i there exists a [0, 1[ such that d tx, ty a max { dx, y, d x, tx, d y, ty, d x, ty, d y, tx }, for all x, y EG; ii there exists x 0 X such that x 0, tx 0 EG; iii EG It t; iv if x, y EG and y, z EG, then x, z EG. In these conditions we have: a existence Fixt ; b uniqueness If, in addition, the following implication holds x, y Fixt x, y EG, then Fixt={x }.
4 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 4 of 11 Proof a Let x 0 X such that x 0, tx 0 EG. By iii we obtain t i x 0, t i+1 x 0 EG, for all i N.Then,byiv,weget t i x 0, t j x 0 EG, for all i, j N with i < j. Since EGweget t i x 0, t j x 0 EG, for all i, j N with i j. 2.1 For n N,leti, j N with 1 i < j n.then d t i x 0, t j x 0 a diam Ox 0 ; n. Notice now that, from the above relation, it follows that there exists k N with k n such that d x 0, t k x 0 = diam Ox 0 ; n. 2.2 In order to show that the sequence t n x 0 n N is Cauchy, let us consider n, m N with n < m.thenwehave d t n x 0, t m x 0 a diam O t n 1 x 0 ; m n +1. By 2.2thereexistsp N with p m n +1suchthat diam O t n 1 x 0 ; m n +1 = d t n 1 x 0, t p t n 1 x 0. Then d t n 1 x 0, t p t n 1 x 0 = d t n 1 x 0, t p+n 1 x 0 = d t t n 2 x 0, t p+1 t n 2 x 0 a diam O t n 2 x 0 ; p +1 a diam O t n 2 x 0 ; m n +2. Thus, we get diam O t n 1 x 0 ; m n +1 a diam O t n 2 x 0 ; m n +2 a n diam Ox 0 ; m. Hence d t n x 0, t m x 0 a n diam Ox 0 ; m. Notice now that diam Ox 0 ; m 1 1 a d x 0, tx 0, for all m N. 2.3
5 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 5 of 11 Indeed, if we take m N arbitrary, then by 2.2, there exists r N such that 1 r m and dx 0, t r x 0 = diamox 0 ; m. Then, using 2.1, we get d x 0, t r x 0 d x 0, tx 0 + d tx 0, t r x 0 d x 0, tx 0 + a diam Ox 0 ; m = d x 0, tx 0 + ad x 0, t r x 0. Hence we have diam Ox 0 ; m = d x 0, t r x a d x 0, tx 0, proving 2.3. Now, we can conclude that d t n x 0, t m x 0 an 1 a d x 0, tx 0, for all n, m N with n < m. 2.4 Thus, 2.4 shows that the sequence t n x 0 n N is Cauchy and, as a consequence of the completeness of the space, it converges to an element x X. We will show now that x Fixt. Notice first that, by the property P, there exists a subsequence x kn n N of x n n N such that x kn, x EGforeachn N. Now, we can write d x, t x d x, x kn+1 + d txkn, t x d x, x kn+1 + a max { d x kn, x, d x kn, tx kn, d x, t x, d x kn, t x, d x, tx kn } d x, x kn+1 + a d xkn, x + d x kn, tx kn + d x, t x + d x, tx kn. Hence d x, t x 1 [ 1 + ad x, x kn+1 + ad xkn, x + adx kn, x kn+1 ]. 1 a Letting n + we get x Fixt. b Suppose that there exist x, y Fixtwithx y. Using i and the additional hypothesis of b, we obtain d x, y = d t x, t y a max { d x, y, d x, t x, d t y, y, d x, t y, d y, t x } = ad x, y, which is a contradiction. Remark 2.1 Notice that, from the proof of the above theorem, it follows that the sequence t n x 0 n N converges to x in X, d.
6 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 6 of 11 Remark 2.2 If in the above theorem, instead of property Pwesupposethatt has closed graphic, then we can reach the same conclusion. Moreover if we suppose that x, y Fixt x, y EG, then we get again Fixt={x }. Based on the above theorem, we can prove now our second main result. Theorem 2.2 Let X, d be a complete metric space and G be a directed graph such that the triple X, d, G satisfies the following property: P for any sequence x n n N Xwithx n xasn, there exists a subsequence x kn n N of x n n N such that x kn, x EG. Let T : X P b X be a multivalued operator. Suppose the following assertions hold: i there exists a [0, 1[ such that δ Tx, Ty a max { dx, y, δ x, Tx, δ y, Ty, D x, Ty, D y, Tx }, for all x, y EG; ii there exists x 0 X such that, for all y Tx 0, we have x 0, y EG; iii EG IT T; iv if x, y EG and y, z EG, then x, z EG. In these conditions we have: a existence FixT=SFixT ; b uniqueness If, in addition, the following implication holds: x, y FixT x, y EG, then FixT=SFixT={x }; c well-posedness of the fixed-point problem If T has closed graphic and for any sequence x n n N, x n X with Hx n, Tx n 0, as n, we have x n, x EG, then the fixed-point problem is well-posed for T with respect to H; d limit shadowing property of T If a < 1 3 and y n n N is a sequence in X such that the following implication holds: D y n+1, Ty n 0, as n y n, x EG, n N, then T has the limit shadowing property. Proof a Let 0 < q < 1 be an arbitrary real number. Notice first that, for any x X, there exists u Tx suchthata q δx, Tx dx, u. In this way, we get an operator t : X X which assigns to each x X the element tx Txwith a q δ x, Tx d x, tx.
7 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 7 of 11 Then, for x, y EG, we have d tx, ty δ Tx, Ty aa q max { a q dx, y, a q δ x, Tx, a q δ y, Ty, a q D x, Ty, a q D y, Tx } a 1 q max { dx, y, d x, tx, d y, ty, d x, ty, d y, tx }. Thus, the operator t satisfies all the hypotheses of Theorem 2.1 and, as a consequence, it has a fixed point x X. Thenx FixT. If we suppose now that there exists x FixT \ S FixT, then, since x, x, from the condition i with y = x, we get δtx aδtx, which implies since a <1thatδTx = 0. Thus Tx={x}.Thisisa contradiction with x FixT \ S FixT, proving that FixT=S FixT. b Suppose that there exist x, y FixT=S FixT. Using i we obtain d x, y = δ T x, T y a max { d x, y, δ x, T x, δ y, T y, D x, T y, D y, T x } = ad x, y, which implies that dx, y =0.HenceFixT=S FixT={x }. c Let x n n N, x n X, be a sequence with the property that Hx n, Tx n 0, as n. It is obvious that Hx n, Tx n = δx n, Tx n. Let x FixT=S FixT. Then Hence d x n, x = δ x n, T x δ x n, Tx n + δ Tx n, T x δ x n, Tx n + a max { d x n, x, δ x n, Tx n, d x n, x, D x, Tx n } δ x n, Tx n + aδ x n, Tx n + ad x n, x. d x n, x 1+a 1 a δ x n, Tx n 0, as n +, and, as a consequence, the fixed-point problem is well-posed for T with respect to H. d Let y n n N be a sequence in X such that Dy n+1, Ty n 0, as n and let x n n N be a sequence of successive approximation of T starting from x 0 X,constructedasinthe proof of Theorem 2.1. We shall prove that dx n, y n 0, as n. Let x FixT=S FixT. Then dx n, y n d x n, x + d x, y n. In what follows we shall prove that dx, y n 0, as n.thenwehave d x, y n+1 δ x, Ty n + D y n+1, Ty n = δ T x, Ty n + D y n+1, Ty n a max { d x, y n, δ yn, Ty n, D x, Ty n, d y n, x } + D y n+1, Ty n aδ y n, Ty n + ad x, y n + D yn+1, Ty n.
8 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 8 of 11 Now, we can write δ y n, Ty n d x, y n + δ x, Ty n = d x, y n + δ T x, Ty n d x, y n + aδ yn, Ty n + ad x, y n. Thus δ y n, Ty n 1+a 1 a d x, y n. If we replace this in the above relation, we get Hence d x, y n+1 2a 1 a d x, y n + D yn+1, Ty n. d y n+1, x 2a 1 a d y n, x + D y n+1, Ty n 2a 2 d y n 1, x + 2a 1 a 1 a D y n, Ty n 1 + D y n+1, Ty n. Continuing this process we shall obtain d y n+1, x 2a n+1 d y 0, x + 1 a n 2a n k D y k+1, Ty k. 1 a k=0 If we consider a n = 2a 1 a n and b n = Dy n+1, Ty n and using the fact that a < 1 3,weobtain, via Cauchy s lemma, dx, y n 0, as n.thusdx, y n 0, as n, and hence, the operator T has the limit shadowing property. Remark 2.3 If in Theorem 2.1, instead of property P, we suppose that every selection t of T has closed graphic, then we obtain FixT=S FixT. Moreoverifwesuppose that the following implication holds: x, y FixT x, y EG, then FixT=SFixT={x }. Proof Since every selection t of T has closed graphic, the conclusion follows by Theorem 2.1,viaRemark2.2. Definition 2.3 Let X, dbeametricspaceandt : X P cl Xbeamultivaluedoperator. By definition the fixed-point problem is well-posed in the generalized sense for T with respect to H if i S Fix T ; ii If x n n N is a sequence in X such that Hx n, Tx n 0,asn, then there d exists a subsequence x kn n N of x n n N such that x kn x,asn.
9 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 9 of 11 Remark 2.4 If in Theorem 2.1 instead of c we suppose the following assumption, c : c If every selection t of T has closed graphic and, in addition, we suppose that for any sequence x n n N X with Hx n, Tx n 0, asn,thereexistsasubsequence x kn n N such that x kn, x EG and Hx kn, Tx kn 0, then the fixed-point problem is well-posed in the generalized sense for T with respect to H. In what follows we shall present some examples of operators satisfying the hypotheses of our main results. Example 2.1 Let X = {0, 1} { 1 : k N } and f : X X given by 2 k x/2, if x { 1 : k N }, f x= 2 k 0, if x {0, 1}. 1 Let V G:=X and EG:={0, 1, 1, 0} {0,, 1 1, 0, 1,, 1,1:k N }. 2 k 2 k 2 k 2 k Then all the hypotheses of Theorem 2.1 are satisfied, Fixt={0} and, if we take x 0 = 1 2, then t n x 0 n N converges to x =0. Example 2.2 Let X = {0, 0, 0, 1, 1, 0} and T : X P b Xgivenby {0, 0}, x = 0, 0, Tx= {0, 0, 1, 0}, x = 0, 1, {0, 0}, x = 1, 0. Let EG:={0, 1; 1, 0, 1, 0; 0, 0}. Notice that FixT=S FixT={0, 0} and all the hypotheses in Theorem 2.2 are satisfied the condition i is verified for a 0, 71. Remark 2.5 It is also important to notice that, if we suppose that there exists x FixT \ S FixT, then, since x, x, from the condition i in the above theorem with y = x, we get δtx aδtx, which implies δtx = 0 since a < 1. This is a contradiction with x FixT \ S FixT, showing that we cannot get fixed points which are not strict fixed points in the presence of the condition i of the above theorem. It is an open problem to prove a similar theorem to the above one for a more general class of multivalued operators T. The next result presents the data dependence of the fixed-point set of a multivalued operator which satisfies a contractive condition of Ćirić type. Theorem 2.3 Let X, d be a complete metric space and G be a directed graph such that the triple X, d, G satisfies property P. Let T 1, T 2 : X P b X be two multivalued operators. Suppose the following assertions hold: i for i {1, 2}, there exist a i [0, 1 such that δ T i x, T i y a max { dx, y, δ x, T i x, δ y, T i y, D x, T i y, D y, T i x }, for all x, y EG;
10 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 10 of 11 ii for each x X and each y Tx we have x, y EG, for i {1, 2}; iii EG IT T; iv if x, y EG and y, z EG, then x, z EG; v there exists η >0such that HT 1 x, T 2 x η for all x X. Under these conditions we have: a FixT i =SFixT i, i {1, 2}; b If, in addition, for i {1, 2}, the following implication holds: x i, y i FixT i x i, y i EG, then FixT i =SFixT i ={x i }, for each i {1, 2}; c HS FixT 1, S FixT 2 η 1 max{a 1,a 2 }. Proof Conclusions a and b are immediate if we apply Theorem 2.2. For c notice that we can prove that for every x 1 S FixT 1, there exists x 2 S FixT 2, such that d x 1, η x 2. 1 a 2 A second relation of this type will be obtained by interchanging the role of T 1 and T 2. Hence, the conclusion follows by the properties of the functional H. Competing interests The authors declare that they have no competing interests. Authors contributions Both authors made equal contribution to this article regarding results, conception and drafting the manuscript. The authors read and approved the final manuscript. Author details 1 Department of Business, Babeş-Bolyai University Cluj-Napoca, Horea street, 7, Cluj-Napoca, , Romania. 2 Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogalniceanu street, 1, Cluj-Napoca, , Romania. Acknowledgements The work of the second author is supported by financial support of a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE Received: 15 October 2013 Accepted: 13 January 2014 Published: 17 Feb 2014 References 1. Jachymski, J: The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc. 136, Gwóźdź-Lukawska, G, Jachymski, J: IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem. J. Math. Anal. Appl. 356, Nicolae, A, O Regan, D, Petruşel, A: Fixed point theorems for single-valued and multivalued generalized contractions in metric spaces endowed with a graph. Georgian Math. J. 18, Beg, I, Butt, AR, Radojevic, S: The contraction principles for set-valued mappings on a metric space with a graph. Comput. Math. Appl. 60, Dinevari, T, Frigon, M: Fixed point results for multivalued contractions on a metric space with a graph. J. Math. Anal. Appl. 405, Border, K: Fixed Point Theorems with Applications to Economic and Game Theory. Cambridge University Press, London Yuan, GX-Z: KKM Theory and Applications in Nonlinear Analysis. Dekker, New York Harjani, J, Sadarangani, K: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 71, Nieto, JJ, Rodríguez-López, R: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22,
11 Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 Page 11 of Nieto, JJ, Rodríguez-López, R: Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. Engl. Ser. 23, Nieto, JJ, Pouso, RL, Rodríguez-López, R: Fixed point theorems in ordered abstract spaces. Proc. Am. Math. Soc. 135, O Regan, D, Petruşel, A: Fixed point theorems in ordered metric spaces. J. Math. Anal. Appl. 341, Petruşel, A, Rus, IA: Fixed point theorems in ordered L-spaces. Proc. Am. Math. Soc. 134, Ran, ACM, Reurings, MC: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc.Am.Math.Soc.132, Rus, IA: Generalized Contractions and Applications. Transilvania Press, Cluj-Napoca Chifu,C,Petruşel, G, Bota, M: Fixed points and strict fixed points for multivalued contractions of Reich type on metric spaces endowed with a graph. Fixed Point Theory Appl. 2013, doi: / Ćirić, LB: A generalization of Banach s contraction principle. Proc. Am. Math. Soc. 45, Petruşel, A, Rus, IA: Well-posedness of the fixed point problem for multivalued operators. In: Carja, O, Vrabie, II eds. Applied Analysis and Differential Equations, pp World Scientific, Hackensack Petruşel, A, Rus, IA, Yao, J-C: Well-posedness in the generalized sense of the fixed point problems for multivalued operators. Taiwan. J. Math. 11, / X Cite this article as: Chifu and Petruşel: Ciric-type δ-contractionsinmetricspacesendowedwithagraph.journal of Inequalities and Applications 2014, 2014:77
Ćirić type fixed point theorems
Stud. Univ. Babeş-Bolyai Math. 59(2014), No. 2, 233 245 Ćirić type fixed point theorems Adrian Petruşel Abstract. The purpose of this paper is to review some fixed point and strict fixed point results
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 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 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 informationA NOTE ON MULTIVALUED MEIR-KEELER TYPE OPERATORS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LI, Number 4, December 2006 A NOTE ON MULTIVALUED MEIR-KEELER TYPE OPERATORS ADRIAN PETRUŞEL AND GABRIELA PETRUŞEL Dedicated to Professor Gheorghe Coman at
More informationFIXED POINT THEORY FOR MULTIVALUED OPERATORS ON A SET WITH TWO METRICS
Fixed Point Theory, Volume 8, No. 1, 2007, 97-104 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html FIXED POINT THEORY FOR MULTIVALUED OPERATORS ON A SET WITH TWO METRICS ADRIAN PETRUŞEL AND IOAN A. RUS
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 for Zamfirescu mappings in metric spaces endowed with a graph
CARPATHIAN J. MATH. 31 2015, No. 3, 297-305 Online version availale at http://carpathian.um.ro Print Edition: ISSN 1584-2851 Online Edition: ISSN 1843-4401 Fixed point theorems for Zamfirescu mappings
More informationFixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces
RESEARCH Open Access Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces Nguyen Van Luong * and Nguyen Xuan Thuan * Correspondence: luonghdu@gmail.com
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 informationFixed point theorems for multivalued nonself Kannan-Berinde G-contraction mappings in complete metric spaces endowed with graphs
The 22 nd Annual Meeting in Mathematics (AMM 2017) Department of Mathematics, Faculty of Science Chiang Mai University, Chiang Mai, Thailand Fixed point theorems for multivalued nonself Kannan-Berinde
More informationResearch Article A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space
Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2010, Article ID 190701, 8 pages doi:10.1155/2010/190701 Research Article A Fixed Point Theorem for Mappings Satisfying a Contractive
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 of ϕ-contraction in metric spaces endowed with a graph
Annals of the University of Craiova, Mathematics and Computer Science Series Volume 374, 2010, Pages 85 92 ISSN: 1223-6934 Fixed point of ϕ-contraction in metric spaces endowed with a graph Florin Bojor
More informationPATA TYPE FIXED POINT THEOREMS OF MULTIVALUED OPERATORS IN ORDERED METRIC SPACES WITH APPLICATIONS TO HYPERBOLIC DIFFERENTIAL INCLUSIONS
U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 4, 216 ISSN 1223-727 PATA TYPE FIXED POINT THEOREMS OF MULTIVALUED OPERATORS IN ORDERED METRIC SPACES WITH APPLICATIONS TO HYPERBOLIC DIFFERENTIAL INCLUSIONS
More informationFixed point theorems for Ćirić type generalized contractions defined on cyclic representations
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 8 (2015), 1257 1264 Research Article Fixed point theorems for Ćirić type generalized contractions defined on cyclic representations Adrian Magdaş
More informationCARISTI TYPE OPERATORS AND APPLICATIONS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVIII, Number 3, September 2003 Dedicated to Professor Gheorghe Micula at his 60 th anniversary 1. Introduction Caristi s fixed point theorem states that
More informationPerov s fixed point theorem for multivalued mappings in generalized Kasahara spaces
Stud. Univ. Babeş-Bolyai Math. 56(2011), No. 3, 19 28 Perov s fixed point theorem for multivalued mappings in generalized Kasahara spaces Alexandru-Darius Filip Abstract. In this paper we give some corresponding
More informationON NADLER S MULTI-VALUED CONTRACTION PRINCIPLE IN COMPLETE METRIC SPACES
ISSN 2066-6594 Ann. Acad. Rom. Sci. Ser. Math. Appl. Vol. 10, No. 1/2018 ON NADLER S MULTI-VALUED CONTRACTION PRINCIPLE IN COMPLETE METRIC SPACES Adrian Petruşel Dedicated to Professor Mihail Megan on
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 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 informationCaristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces
International Journal of Mathematical Analysis Vol. 11, 2017, no. 6, 267-275 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.717 Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric
More informationSeminar on Fixed Point Theory Cluj-Napoca, Volume 1, 2000, nodeacj/journal.htm
Seminar on Fixed Point Theory Cluj-Napoca, Volume 1, 2000, 63-68 http://www.math.ubbcluj.ro/ nodeacj/journal.htm FIXED POINT THEOREMS FOR MULTIVALUED EXPANSIVE OPERATORS Aurel Muntean Carol I High School
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 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 informationAPPROXIMATING FIXED POINTS OF NONSELF CONTRACTIVE TYPE MAPPINGS IN BANACH SPACES ENDOWED WITH A GRAPH
DOI: 10.1515/auom-2016-0026 An. Şt. Univ. Ovidius Constanţa Vol. 24(2),2016, 27 43 APPROXIMATING FIXED POINTS OF NONSELF CONTRACTIVE TYPE MAPPINGS IN BANACH SPACES ENDOWED WITH A GRAPH Laszlo Balog, Vasile
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 informationFIXED POINTS AND CONTINUITY OF ALMOST CONTRACTIONS
FIXED POINTS AND CONTINUITY OF ALMOST CONTRACTIONS VASILE BERINDE AND MĂDĂLINA PĂCURAR Abstract. Almost contractions form a class of generalized contractions that includes several contractive type mappings
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 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 informationOn coupled generalised Banach and Kannan type contractions
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 5 (01, 59 70 Research Article On coupled generalised Banach Kannan type contractions B.S.Choudhury a,, Amaresh Kundu b a Department of Mathematics,
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 informationMONOTONE GENERALIZED WEAK CONTRACTIONS IN PARTIALLY ORDERED METRIC SPACES
Fixed Point Theory, 11(2010), No. 2, 375-382 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html MONOTONE GENERALIZED WEAK CONTRACTIONS IN PARTIALLY ORDERED METRIC SPACES R. SAADATI AND S.M. VAEZPOUR Department
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 informationarxiv: v1 [math.gn] 5 Apr 2013
Fixed Points for Ćirić-G-Contractions in Uniform Spaces Endowed with a Graph arxiv:1304.1721v1 [math.gn] 5 Apr 2013 Aris Aghanians 1, Kamal Fallahi 1, Kourosh Nourouzi 1, Ram U Verma 2 1 Department of
More informationA novel approach to Banach contraction principle in extended quasi-metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 3858 3863 Research Article A novel approach to Banach contraction principle in extended quasi-metric spaces Afrah A. N. Abdou a, Mohammed
More informationOn quasi-contractions in metric spaces with a graph
Hacettepe Journal of Mathematics and Statistics Volume 45 (4) (2016), 1033 1047 On quasi-contractions in metric spaces with a graph Kamal Fallahi and Aris Aghanians Keywords: Abstract In the present work,
More informationA NEW PERSPECTIVE FOR MULTIVALUED WEAKLY PICARD OPERATORS. Gonca Durmaz and Ishak Altun
PUBLICATIONS DE L INSTITUT MATHÉMATIQUE Nouvelle série, tome 101(115) (2017), 197 204 https://doi.org/10.2298/pim1715197d A NEW PERSPECTIVE FOR MULTIVALUED WEAKLY PICARD OPERATORS Gonca Durmaz and Ishak
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 informationResearch Article Fixed Point Theorems in Cone Banach Spaces
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009, Article ID 609281, 9 pages doi:10.1155/2009/609281 Research Article Fixed Point Theorems in Cone Banach Spaces Erdal Karapınar
More informationCOMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES
STUDIA UNIV. BABEŞ BOLYAI MATHEMATICA Volume XLVII Number 1 March 00 COMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES 1. Introduction The purpose of this paper is to prove
More informationarxiv: v1 [math.gm] 31 May 2016
arxiv:1606.0590v1 [math.gm] 31 May 016 Common Fixed Points of Weakly Commuting Multivalued Mappings on Domain of Sets Endowed with Directed Graph Sergei Silvestrov 1 and Talat Nazir 1, (1) Division of
More informationFixed point theorems for Kannan-type maps
Ume Fixed Point Theory and Applications (2015) 2015:38 DOI 10.1186/s13663-015-0286-5 R E S E A R C H Open Access Fixed point theorems for Kannan-type maps Jeong Sheok Ume * * Correspondence: jsume@changwon.ac.kr
More informationFixed points of monotone mappings and application to integral equations
Bachar and Khamsi Fixed Point Theory and pplications (15) 15:11 DOI 1.1186/s13663-15-36-x RESERCH Open ccess Fixed points of monotone mappings and application to integral equations Mostafa Bachar1* and
More informationFIXED POINT THEOREMS OF KRASNOSELSKII TYPE IN A SPACE OF CONTINUOUS FUNCTIONS
Fixed Point Theory, Volume 5, No. 2, 24, 181-195 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm FIXED POINT THEOREMS OF KRASNOSELSKII TYPE IN A SPACE OF CONTINUOUS FUNCTIONS CEZAR AVRAMESCU 1 AND CRISTIAN
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 informationSOME RESULTS CONCERNING THE MULTIVALUED OPTIMIZATION AND THEIR APPLICATIONS
Seminar on Fixed Point Theory Cluj-Napoca, Volume 3, 2002, 271-276 http://www.math.ubbcluj.ro/ nodeacj/journal.htm SOME RESULTS CONCERNING THE MULTIVALUED OPTIMIZATION AND THEIR APPLICATIONS AUREL MUNTEAN
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 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 informationFixed Point Theorems for Mapping Having The Mixed Monotone Property
International Archive of Applied Sciences and Technology Int. Arch. App. Sci. Technol; Vol 5 [2]June 2014: 19-23 2014 Society of Education India [ISO9001: 2008 Certified Organization] www.soeagra.co/iaast.html
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 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 theorems for a class of maps in normed Boolean vector spaces
RESEARCH Fixed point theorems for a class of maps in normed Boolean vector spaces Swaminath Mishra 1, Rajendra Pant 1* and Venkat Murali 2 Open Access * Correspondence: pant. rajendra@gmail.com 1 Department
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 informationRelevant Classes of Weakly Picard Operators
DOI: 10.1515/awutm -2016-0019 Analele Universităţii de Vest, Timişoara Seria Matematică Informatică LIV, 2, (2016), 131 147 Relevant Classes of Weakly Picard Operators Ioan A. Rus Abstract. In this paper
More informationCommon fixed point of multivalued graph contraction in metric spaces
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 225-230 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.309 Common fixed point of multivalued graph contraction in metric spaces Masoud
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 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 informationSomeresultsonfixedpointsofα-ψ-Ciric generalized multifunctions
Mohammadi et al. Fixed Point Theory and Applications 013, 013:4 R E S E A R C H Open Access Someresultsonfixedpointsofα-ψ-Ciric generalized multifunctions B Mohammadi 1,SRezapour and N Shahzad 3* * Correspondence:
More informationAvailable online at J. Nonlinear Sci. Appl., 10 (2017), Research Article
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 2719 2726 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa An affirmative answer to
More informationRemark on a Couple Coincidence Point in Cone Normed Spaces
International Journal of Mathematical Analysis Vol. 8, 2014, no. 50, 2461-2468 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.49293 Remark on a Couple Coincidence Point in Cone Normed
More informationFIXED POINTS FOR MULTIVALUED CONTRACTIONS WITH RESPECT TO A w-distance.
Scientiae Mathematicae Japonicae Online, e-2009, 611 619 611 FIXED POINTS FOR MULTIVALUED CONTRACTIONS WITH RESPECT TO A w-distance. Received April 22, 2008; Revised November 9, 2009 Abstract. The aim
More informationFixed Point Theory in Reflexive Metric Spaces
Babeş-Bolyai University Cluj-Napoca Department of Mathematics and University of Seville Department of Mathematical Analysis Fixed Point Theory in Reflexive Metric Spaces Ph.D. Thesis Summary Adriana-Maria
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 informationResearch Article Fixed Points for Multivalued Mappings and the Metric Completeness
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009, Article ID 97295, 15 pages doi:10.1155/2009/97295 Research Article Fixed Points for Multivalued Mappings and the Metric Completeness
More informationCOMMON FIXED POINTS IN b-metric SPACES ENDOWED WITH A GRAPH. Sushanta Kumar Mohanta. 1. Introduction
MATEMATIQKI VESNIK 68, 2 (2016), 140 154 June 2016 originalni nauqni rad research paper COMMON FIXED POINTS IN b-metric SPACES ENDOWED WITH A GRAPH Sushanta Kumar Mohanta Abstract. We discuss the existence
More informationResearch Article Some New Fixed-Point Theorems for a (ψ, φ)-pair Meir-Keeler-Type Set-Valued Contraction Map in Complete Metric Spaces
Applied Mathematics Volume 2011, Article ID 327941, 11 pages doi:10.1155/2011/327941 Research Article Some New Fixed-Point Theorems for a (ψ, φ)-pair Meir-Keeler-Type Set-Valued Contraction Map in Complete
More informationSome notes on a second-order random boundary value problem
ISSN 1392-5113 Nonlinear Analysis: Modelling and Control, 217, Vol. 22, No. 6, 88 82 https://doi.org/1.15388/na.217.6.6 Some notes on a second-order random boundary value problem Fairouz Tchier a, Calogero
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 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 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 informationA multivalued version of Krasnoselskii s theorem in generalized Banach spaces
DOI: 1.2478/auom-214-41 An. Şt. Univ. Ovidius Constanţa Vol. 22(2,214, 177 192 A multivalued version of Krasnoselskii s theorem in generalized Banach spaces Ioan-Radu PETRE Abstract The purpose of this
More informationEXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS
EXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS Adriana Buică Department of Applied Mathematics Babeş-Bolyai University of Cluj-Napoca, 1 Kogalniceanu str., RO-3400 Romania abuica@math.ubbcluj.ro
More informationA Direct Proof of Caristi s Fixed Point Theorem
Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289-2294 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.66190 A Direct Proof of Caristi s Fixed Point Theorem Wei-Shih Du Department
More informationAvailable online at Adv. Fixed Point Theory, 3 (2013), No. 4, ISSN:
Available online at http://scik.org Adv. Fixed Point Theory, 3 (2013), No. 4, 595-599 ISSN: 1927-6303 A COMMON FIXED POINT THEOREM UNDER ϕ-contractive CONDITIONS PH.R. SINGH 1,, AND M.R. SINGH 2, 1 Department
More informationJournal of Mathematical Analysis and Applications. IFS on a metric space with a graph structure and extensions of the Kelisky Rivlin theorem
J. Math. Anal. Appl. 356 2009) 453 463 Contents lists available at ScienceDirect Journal of Mathematical Analysis and Applications www.elsevier.com/locate/jmaa IFS on a metric space with a graph structure
More informationKannan Fixed Point Theorem on Generalized Metric Space with a Graph
Applied Mathematical Sciences, Vol. 3, 209, no. 6, 263-274 HIKARI Ltd, www.m-hikari.com https://doi.org/0.2988/ams.209.9226 Kannan Fixed Point Theorem on Generalized Metric Space with a Graph Karim Chaira
More informationFixed point results for {α, ξ}-expansive locally contractive mappings
Ahmad et al. Journal of Inequalities and Applications 2014, 2014:364 R E S E A R C H Open Access Fixed point results for {α, ξ}-expansive locally contractive mappings Jamshaid Ahmad 1*, Ahmed Saleh Al-Rawashdeh
More informationFixed points of multivalued mappings in modular function spaces with a graph
Alfuraidan Fixed Point Theory and Applications (2015) 2015:42 DOI 10.1186/s13663-015-0292-7 R E S E A R C H Open Access Fixed points of multivalued mappings in modular function spaces with a graph Monther
More informationCOMMON RANDOM FIXED POINTS UNDER QUASI CONTRACTION CONDITIONS IN SYMMETRIC SPACES
Available online at http://scik.org Adv. Fixed Point Theory, 7 (2017), No. 3, 451-457 ISSN: 1927-6303 COMMON RANDOM FIXED POINTS UNDER QUASI CONTRACTION CONDITIONS IN SYMMETRIC SPACES Maulana Azad National
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 POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS
Fixed Point Theory, 14(2013), No. 2, 301-312 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html FIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS VASILE BERINDE AND MĂDĂLINA PĂCURAR Department
More informationResearch Article Some Generalizations of Fixed Point Results for Multivalued Contraction Mappings
International Scholarly Research Network ISRN Mathematical Analysis Volume 2011, Article ID 924396, 13 pages doi:10.5402/2011/924396 Research Article Some Generalizations of Fixed Point Results for Multivalued
More informationFIXED POINTS RESULTS OF DOMINATED MAPPINGS ON A CLOSED BALL IN ORDERED PARTIAL METRIC SPACES WITHOUT CONTINUITY
U.P.B. Sci. Bull., Series A, Vol. 76, Iss. 2, 2014 ISSN 1223-27 FIXED POINTS RESULTS OF DOMINATED MAPPINGS ON A CLOSED BALL IN ORDERED PARTIAL METRIC SPACES WITHOUT CONTINUITY Muhammad Arshad 1, Akbar
More informationPICARD OPERATORS IN b-metric SPACES VIA DIGRAPHS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 3(2017), Pages 42-51. PICARD OPERATORS IN b-metric SPACES VIA DIGRAPHS SUSHANTA KUMAR MOHANTA
More informationKannan mappings vs. Caristi mappings: An easy example
Kannan mappings vs. Caristi mappings: An easy example Carmen Alegre, S. R. WATS 2016, Valencia June 22, 2016 1 / 13 In 1922, Banach published his famous fixed point theorem wich is stated as follows. Theorem
More informationResearch Article The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with w-distances
Applied Mathematics Volume 2012, Article ID 161470, 11 pages doi:10.1155/2012/161470 Research Article The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with w-distances Hossein
More informationResearch Article Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications
Abstract and Applied Analysis Volume 2012, Article ID 479438, 13 pages doi:10.1155/2012/479438 Research Article Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and
More informationStability of Noor Iteration for a General Class of Functions in Banach Spaces
Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 51, 2 2012 19 25 Stability of Noor Iteration for a General Class of Functions in Banach Spaces Alfred Olufemi BOSEDE Department of Mathematics,
More informationFixed Point Problems for α-ψ-weakly Contractive Operators on KST Spaces
Filomat 31:14 (017), 4441 4454 https://doi.org/10.98/fil1714441g Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Problems
More informationStrong convergence theorems for total quasi-ϕasymptotically
RESEARCH Open Access Strong convergence theorems for total quasi-ϕasymptotically nonexpansive multi-valued mappings in Banach spaces Jinfang Tang 1 and Shih-sen Chang 2* * Correspondence: changss@yahoo.
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 informationAvailable online at J. Math. Comput. Sci. 4 (2014), No. 5, ISSN:
Available online at http://scik.org J. Math. Comput. Sci. 4 (2014), No. 5, 826-833 ISSN: 1927-5307 A COINCIDENCE POINT THEREM FOR F-CONTRACTIONS ON METRIC SPACES EQUIPPED WITH AN ALTERED DISTANCE RAKESH
More informationFIXED POINTS OF MULTIVALUED MAPPINGS IN CERTAIN CONVEX METRIC SPACES. Tomoo Shimizu Wataru Takahashi. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 8, 1996, 197 203 FIXED POINTS OF MULTIVALUED MAPPINGS IN CERTAIN CONVEX METRIC SPACES Tomoo Shimizu Wataru Takahashi
More informationResearch Article Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems
Abstract and Applied Analysis Volume 211, Article ID 54335, 13 pages doi:1.1155/211/54335 Research Article Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems J. Caballero,
More informationA fixed point theorem for weakly Zamfirescu mappings
A fixed point theorem for weakly Zamfirescu mappings David Ariza-Ruiz Dept. Análisis Matemático, Fac. Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain Antonio Jiménez-Melado Dept.
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 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 COINCIDENCE AND FIXED POINT THEOREMS FOR SEMI-QUASI CONTRACTIONS
Fixed Point Theory, 17(2016), No. 2, 449-456 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html A COINCIDENCE AND FIXED POINT THEOREMS FOR SEMI-QUASI CONTRACTIONS RAJENDRA PANT, S.L. SINGH AND S.N. MISHRA
More informationON RANDOM FIXED POINTS IN RANDOM CONVEX STRUCTURES
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LIII, Number 2, June 2008 ON RANDOM FIXED POINTS IN RANDOM CONVEX STRUCTURES ASHOK GANGULY, RAGHVENDRA SINGH CHANDEL, AND RAVINDRA PARSAI Abstract. In this
More information