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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: 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: 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: 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: 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: 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.Article Citation - WoS: 7Citation - Scopus: 9Cyclic Contractions and Related Fixed Point Theorems on g-metric Spaces(Natural Sciences Publishing Corp-nsp, 2014) Bilgili, N.; Erhan, I. M.; Karapinar, E.; Turkoglu, D.Very recently, Jleli and Samet [53] and Samet et. al. [52] reported that some fixed point result in G-metric spaces can be derived from the fixed point theorems in the setting of usual metric space. In this paper, we prove the existence and uniqueness of fixed points of certain cyclic mappings in the context of G-metric spaces that can not be obtained by usual fixed point results via techniques used in [53,52]. We also give an example to illustrate our statements.Article Citation - WoS: 33Citation - Scopus: 34Iterative Approximation of Fixed Points for Presic Type f-contraction Operators(Univ Politehnica Bucharest, Sci Bull, 2016) Abbas, M.; Karapınar, Erdal; Berzig, M.; Nazir, T.; Karapinar, E.; Karapınar, Erdal; Mathematics; Mathematics; MathematicsWe study the convergence of the Presic type k-step iterative process for a class of operators f : X-k -> X satisfying Presic type F-contractive condition in the setting of metric spaces. As an applications of the result presented herein, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.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: 63Citation - Scopus: 61Fixed Point Theorem for Cyclic Maps on Partial Metric Spaces(Natural Sciences Publishing Corp-nsp, 2012) Karapinar, E.; Erhan, I. M.; Ulus, A. Yildiz; MathematicsIn this paper, a class of cyclic contractions on partial metric spaces is introduced. A fixed point theorem for cyclic contractions on partial metric spaces satisfying (psi, phi) contractive condition, and illustrative examples are given.
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