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Article Citation - WoS: 178Citation - Scopus: 184Couple fixed point theorems for nonlinear contractions in cone metric spaces(Pergamon-elsevier Science Ltd, 2010) Karapinar, ErdalThe notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham (2006) in [13]. In this manuscript, some results of Lakshmikantham and Ciric (2009) in [5] are extended to the class of cone metric spaces. (C) 2010 Elsevier Ltd. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 63Discussion on Α - Ψ Contractions on Generalized Metric Spaces(Hindawi Ltd, 2014) Karapinar, ErdalWe discuss the existence and uniqueness of fixed points of alpha - psi contractive mappings in complete generalized metric spaces, introduced by Branciari. Our results generalize and improve several results in the literature.Article Citation - WoS: 37Citation - Scopus: 44Best Proximity Points of Kannan Type Cyclic Weak Ø-Contractions in Ordered Metric Spaces(Ovidius University, 2012) Karapinar,E.In this manuscript, the existence of the best proximity of Kannan Type cyclic weak ø -contraction in ordered metric spaces is investigated. Some results of Rezapour-Derafshpour-Shahzad [22] are generalized.Article Citation - WoS: 63Citation - Scopus: 76Α-Ψ Contraction Type Mappings and Some Related Fixed Point Results(Univ Nis, Fac Sci Math, 2014) Karapinar, ErdalIn this paper, we consider a generalization of alpha-psi-Geraghty contractions and investigate the existence and uniqueness of fixed point for the mapping satisfying this condition. We illustrate an example and an application to support our results. In particular, we extend, improve and generalize some earlier results in the literature on this topic.Article Citation - WoS: 60Citation - Scopus: 67Some Nonunique Fixed Point Theorems of Ciric Type on Cone Metric Spaces(Hindawi Publishing Corporation, 2010) Karapinar, ErdalSome results of (Ciric, 1974) on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally T complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.Article Citation - WoS: 11Citation - Scopus: 7Edelstein Type Fixed Point Theorems(Tusi Mathematical Research Group, 2011) Karapinar,E.; Karapınar, Erdal; Karapınar, Erdal; Mathematics; MathematicsRecently, Suzuki [Nonlinear Anal. 71 (2009), no. 11, 5313-5317.] published a paper on which Edelstein’s fixed theorem was generalized. In this manuscript, we give some theorems which are the generalization of the fixed theorem of Suzuki’s Theorems and thus Edelstein’s result [J. London Math. Soc. 37 (1962), 74-79]. © 2011, Duke University Press. All rights reserved.Book Part Citation - Scopus: 14A Short Survey on Dislocated Metric Spaces Via Fixed-Point Theory(Springer Singapore, 2017) Karapinar,E.In this survey, we collect and combine basic notions and results for the fixed points of certain operators in the frame of dislocated metric (respectively, b-metric) spaces. By preparing a fundamental source, we shall aim to show that there are some rooms for researchers in this interesting and applicable research direction. © Springer Nature Singapore Pte Ltd. 2017. All rights reserved.Article Citation - WoS: 54Citation - Scopus: 62Weak ø-Contraction on partial metric spaces(Eudoxus Press, LLC, 2012) Karapinar,E.In this manuscript, the notion of weak ø-contraction is considered on partial metric space. It is shown that a self mapping T on a complete partial metric space X has a fixed point if they satisfied weak ø-contraction. © 2012 EUDOXUS PR20E6SS, LLC.Article Citation - WoS: 142Citation - Scopus: 139Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces(Springer international Publishing Ag, 2011) Karapinar, ErdalIn this article, lower semi-continuous maps are used to generalize Cristi-Kirk's fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces. Some more general results are also obtained in partial metric spaces. 2000 Mathematics Subject Classification 47H10,54H25Article Citation - WoS: 70Citation - Scopus: 70Best Proximity Points of Cyclic Mappings(Pergamon-elsevier Science Ltd, 2012) Karapinar, ErdalIn this this manuscript, we proved that the existence of best proximity points for the cyclic operators T defined on a union of subsets A, B of a uniformly convex Banach space X with T (A) subset of B, T(B) subset of A and satisfying the condition parallel to Tx - Yy parallel to <= alpha/3[parallel to x-y parallel to + parallel to Tx - x parallel to + parallel to Ty - y parallel to] + (1 - alpha)diam(A, B) for alpha is an element of (0, 1) and for all x is an element of A, for all y is an element of B, where diam(A, B) = inf{parallel to x - y parallel to : x is an element of A, y is an element of B}. (C) 2012 Elsevier Ltd. All rights reserved.
