7 results
Search Results
Now showing 1 - 7 of 7
Article Citation - WoS: 199Citation - Scopus: 195Existence and uniqueness of a common fixed point on partial metric spaces(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, T.; Karapinar, E.; Tas, K.In this work, a general form of the weak phi-contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings S, T on a complete partial metric space X have a common fixed point if it is a generalized weak phi-contraction. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 9Cyclic (φ)-Contractions in Uniform Spaces and Related Fixed Point Results(Hindawi Ltd, 2014) Hussain, N.; Karapinar, E.; Sedghi, S.; Shobkolaei, N.; Firouzian, S.First, we define cyclic (phi)-contractions of different types in a uniform space. Then, we apply these concepts of cyclic (phi)-contractions to establish certain fixed and common point theorems on a Hausdorff uniform space. Some more general results are obtained as corollaries. Moreover, some examples are provided to demonstrate the usability of the proved theorems.Article Citation - WoS: 2Citation - Scopus: 1On Reich Type Λ - Α-Nonexpansive Mapping in Banach Spaces With Applications To l1<(Univ Politecnica Valencia, Editorial Upv, 2018) Belbaki, Rabah; Karapinar, E.; Ould-Hammouda, AmarIn this manuscript we introduce a new class of monotone generalized nonexpansive mappings and establish some weak and strong convergence theorems for Krasnoselskii iteration in the setting of a Banach space with partial order. We consider also an application to the space L-1([0, 1]). Our results generalize and unify the several related results in the literature.Article Citation - WoS: 10Citation - Scopus: 12Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications To Impulsive Differential and Difference Equations(Hindawi Ltd, 2013) De la Sen, M.; Karapinar, E.This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.Article Citation - WoS: 10Citation - Scopus: 16Cyclic Contractions on g-metric Spaces(Hindawi Ltd, 2012) Karapinar, E.; Yildiz-Ulus, A.; Erhan, I. M.Conditions for existence and uniqueness of fixed points of two types of cyclic contractions defined on G-metric spaces are established and some illustrative examples are given. In addition, cyclic maps satisfying integral type contractive conditions are presented as applications.Article Citation - WoS: 3Citation - Scopus: 3On Modified Α-Φ Meir-Keeler Contractive Mappings(Univ Nis, Fac Sci Math, 2014) Salimi, P.; Hussain, N.; Roldan, A.; Karapinar, E.Samet et al. [Nonlinear Anal. 75: 2154-2165, 2012] introduced and studied alpha-psi-contractive mappings. More recently Salimi, et al. [Fixed Point Theory Appl., 2013: 151] modified the notion of alpha-psi-contractive mappings and improved the fixed point theorems in [20, 32]. Here we utilize these notions to establish fixed point results for modified alpha-phi-asymmetric Meir-Keeler contractions and triangular alpha-admissible mappings defined on G-metric and cone G-metric spaces. Several interesting consequences of our theorems are also provided here to illustrate the usability of the obtained results.Article Citation - WoS: 4Citation - Scopus: 6A Note on A Rational Form Contractions With Discontinuities at Fixed Points(House Book Science-casa Cartii Stiinta, 2020) Karapinar, E.In this paper, we investigate one of the classical problems of the metric fixed point theory: Whether there is a contraction condition which does not force the mapping to be continuous at the fixed point. We propose a contraction conditions in rational form that has a unique fixed point but not necessarily continuous at the given fixed point.
