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Article Citation - WoS: 13Citation - Scopus: 11Fixed Point Theorems for (α, Ψ)-Meir Mappings(International Scientific Research Publications, 2015-11-05) Redjel,N.; Dehici,A.; Karapınar,E.; Erhan,İ.M.In this paper, we establish fixed point theorems for a (α, ψ)-Meir-Keeler-Khan self mappings. The main result of our work is an extension of the theorem of Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste. Vol VIII, Fase., 10 (1976), 1-4]. We also give some consequences. © 2015 All rights reserved.Article Citation - WoS: 21Citation - Scopus: 23On (α, Ψ)-<i>k</I>-contractions in the Extended <i>b</I>-metric Space(Univ Nis, Fac Sci Math, 2018) Alqahtani, Badr; Karapinar, Erdal; Ozturk, AliIn this paper, we introduce a notion of (alpha, psi)-K-contraction in the setting of extended b-metric spaces and investigate the existence of a fixed point. The presented results generalize and unify a number of well-known fixed point theorem mainly in two distinct aspects; in the sense of the contraction conditions and in the frame of abstract spaces.Article Citation - WoS: 5Citation - Scopus: 6Revisiting of Some Outstanding Metric Fixed Point Theorems Via <i>e</I>-contraction(Ovidius Univ Press, 2018-12-01) Fulga, Andreea; Karapinar, ErdalIn this paper, we introduce the notion of alpha-psi-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.Article Citation - WoS: 37Citation - Scopus: 36A Fixed Point Theorem and the Ulam Stability in Generalized Dq-Metric Spaces(Academic Press inc Elsevier Science, 2018-11) Brzdek, Janusz; Karapinar, Erdal; Petrusel, AdrianWe prove a fixed point theorem for function spaces, that is a very efficient and convenient tool for the investigations of various operator inequalities connected to Ulam stability issues, in classes of functions taking values in various spaces (e.g., in ultrametric spaces, dq-metric spaces, quasi-Banach spaces, and p-Banach spaces). The theorem is a natural generalization and extension of the classical Banach Contraction Principle and some other more recent results. (C) 2018 Elsevier Inc. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 54Common Fixed Point Results on an Extended B-Metric Space(Springeropen, 2018-07-03) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we investigate the existence of common fixed points of a certain mapping in the frame of an extended b-metric space. The given results cover a number of well-known fixed point theorems in the literature. We state some examples to illustrate our results.Article Citation - WoS: 1Citation - Scopus: 1Discussion on the Fixed Point Problems With Constraint Inequalities(Springeropen, 2018-08-30) Alqahtani, Badr; Lashkaripour, Rahmatollah; Karapinar, Erdal; Hamzehnejadi, JavadIn this paper, we introduce the concept of comparable complete metric spaces and consider some fixed point theorems for mappings in the setting of incomplete metric spaces. We obtain the results of Ansari et al. [J. Fixed Point Theory Appl. 20:26, 2018] with weaker conditions. Moreover, we provide some corollaries and examples show that our main result is a generalization of existing results in the literature.Article Citation - WoS: 43A Common Fixed Point Theorem for Cyclic Operators on Partial Metric Spaces(Univ Nis, Fac Sci Math, 2012) Karapinar, Erdal; Karapınar, Erdal; Shobkolaei, Nabi; Sedghi, Shaban; Vaezpour, S. Mansour; Karapınar, Erdal; Mathematics; MathematicsIn this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.Article Citation - WoS: 79Citation - Scopus: 82A Generalized Contraction Principle With Control Functions on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2012-02) Abdeljawad, Thabet; Karapinar, Erdal; Tas, KenanPartial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 69An Ulam stability result on quasi-<i>b</i>-metric-like spaces(Sciendo, 2016-01-01) Alsulami, Hamed H.; Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.In this paper a class of general type alpha-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.Article Citation - WoS: 15Citation - Scopus: 13Matkowski Theorems in the Context of Quasi-Metric Spaces and Consequences on <i>g</I>-metric Spaces(Sciendo, 2016-01-01) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Samet, BessemIn this paper, we prove the characterization of a Matkowski's theorem in the setting of quasi-metric spaces. As a result, we observe that some recent fixed point results in the context of G-metric spaces are consequences of our main result.