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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 Generalized Partial Metric Spaces With a Fixed Point Theorem(Islamic Azad Univ, Shiraz Branch, 2019) Aydi, H.; Karapinar, E.In this paper, we introduce the notion of extended partial metric space and we present some fixed point theorems in generalized partial metric spaces involving linear and nonlinear contractions.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 - Scopus: 11Some Fixed Points Results on Branciari Metric Spaces Via Implicit Functions(North University of Baia Mare, 2015) Karapinar, E.In this paper, we introduce the notion of α-implicit contractive mapping of integral type in the context of Branciari metric spaces. The results of this paper, generalize and improve several results on the topic in literature. We give an example to illustrate our results. © 2015, North University of Baia Mare. All rights reserved.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: 7Citation - Scopus: 9A New Approach To the Existence and Uniqueness of Solutions for A Class of Nonlinear Q-Fractional Boundary Value Problems(Institute of Applied Mathematics of Baku State University, 2025) Karapinar, E.; Sevinik-Adiguzel, R.; Aksoy, U.; Erhan, I. M.The object of this study is a boundary value problem associated with a q-difference equation of fractional order. The existence and uniqueness of a solution in the case of multi-point boundary conditions is studied from the viewpoint of fixed point theory. An integral equation equivalent to the boundary value problem is derived and the fixed points of the related integral operator are investigated by using a contractive condition involving a comparison function. The Ulam-Hyers stability of the problem is also discussed. Theoretical results are followed by a particular example.Article Citation - WoS: 47Citation - Scopus: 52Some Remarks on Multidimensional Fixed Point Theorems(House Book Science-casa Cartii Stiinta, 2014) Roldan, A.; Martinez-Moreno, J.; Roldan, C.; Karapinar, E.; MathematicsIn this paper, we show that most of the multidimensional (including coupled, tripled, quadrupled) fixed point theorems in the context of (ordered) metric spaces are, in fact, immediate consequences of well-known fixed point theorems in the literature.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: 13Citation - Scopus: 13Coincidence Point Theorems on Quasi-Metric Spaces Via Simulation Functions and Applications To g-metric Spaces(Springer Basel Ag, 2018) Lopez de Hierro, A. F. Roldan; Karapinar, E.; O'Regan, D.In this paper, we present some coincidence point results in the framework of quasi-metric spaces using contractive conditions involving simulation functions. As consequences, we are able to particularize these results to a variety of situations including G-metric spaces. The results presented in this paper generalize and extend several comparable results in the existing literature. In addition, some examples are given.Article Citation - WoS: 5Citation - Scopus: 4Existence and Uniqueness of Common Coupled Fixed Point Results Via Auxiliary Functions(Springer Singapore Pte Ltd, 2014) Chandok, S.; Karapinar, E.; Khan, M. Saeed; MathematicsThe purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed g-monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.
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