Browsing by Author "Karapinar,E."
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Article Citation Count: 42Best proximity points of Kannan type cyclic weak ø-contractions in ordered metric spaces(Ovidius University, 2012) Karapınar, Erdal; MathematicsIn 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 Count: 3Coincidence points for expansive mappings under c-distance in cone metric spaces(2012) Karapınar, Erdal; Karapinar,E.; Moradi,S.; MathematicsWe establish some fixed (common fixed) and coincidence point results for mappings verifying some expansive type contractions in cone metric spaces with the help of the concept of a c-distance. Our results generalize, extend, and unify several well-known comparable results in the literature. Some examples are also presented. Copyright © 2012 Hassen Aydi et al.Article Citation Count: 6Edelstein type fixed point theorems(Tusi Mathematical Research Group, 2011) Karapınar, Erdal; 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.Article Citation Count: 10A fixed point result for Boyd-Wong cyclic contractions in partial metric spaces(2012) Karapınar, Erdal; Karapinar,E.; MathematicsA fixed point theorem involving Boyd-Wong-type cyclic contractions in partial metric spaces is proved. We also provide examples to support the concepts and results presented herein. Copyright © 2012 Hassen Aydi and Erdal Karapinar.Article Citation Count: 24Fixed point theorem on partial metric spaces involving rational expressions(University of Miskolc, 2013) Karapınar, Erdal; Shatanawi,W.; Tas,K.; MathematicsWe establish a fixed point theorem involving a rational expression in a complete partial metric space. Our result generalizes a well-known result in (usual) metric spaces. Also, we introduce an example to illustrate the usability of our result. © Miskolc University Press.Article Citation Count: 7Fixed point theory for cyclic generalized (φ-ϕ)-contraction mappings(Springer-Verlag Italia s.r.l., 2013) Karapınar, Erdal; Moradi,S.; MathematicsFixed point results are presented for cyclic generalized (φ{symbol}-φ)-contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Ćirić, Moradi and Khojasteh, and Karapinar. © 2012 Università degli Studi di Ferrara.Article Citation Count: 14Fixed point theory for the α-admissible meir-keeler- type set contractions having KKM* property on almost convex sets(Natural Sciences Publishing, 2017) Karapınar, Erdal; Abkar,A.; Ghods,S.; Karapinar,E.; MathematicsThe purpose of this paper is to study fixed points for the KKM* family satisfying the a-admissible Meir-Keeler-type set contractions with respect to the set measure σp of noncompactness in the context of Hausdorff topological vector spaces. Our results generalize or improve many recent fixed point theorems for the KKM family in the literature. Subject class: [2000]46T99,47H10, 54C60, 54H25, 55M20. © 2017 NSP.Book Citation Count: 97Fixed point theory in metric type spaces(Springer International Publishing, 2016) Karapınar, Erdal; Karapinar,E.; O’regan,D.; Roldán-López-De-Hierro,A.F.; MathematicsWritten by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research. © David Ralph 2015.Article Citation Count: 10Fixed points results for α -admissible mapping of integral type on generalized metric spaces(Hindawi Publishing Corporation, 2015) Karapınar, Erdal; MathematicsWe introduce generalized (α,ψ)-contractive mappings of integral type in the context of generalized metric spaces. The results of this paper generalize and improve several results on the topic in literature. © 2015 Erdal Karapinar.Article Citation Count: 4A generalization of the Meir–Keeler type contraction(Elsevier B.V., 2012) Karapınar, Erdal; Karapinar,E.; Thanh,T.D.; MathematicsIn this paper, we prove a fixed point theorem which has applications on maps called T-contractions which include a class that satisfies the Meir–Keeler type contractive condition. We also present an example that illustrates that T-contractions are a natural extension of the Meir–Keeler type contraction. © 2012Article Citation Count: 1Imperative remarks for "on common coupled fixed point theorems for comparable mappings in ordered partially metric spaces" and an answer to the question: How to smooth it away(Hindawi Publishing Corporation, 2015) Karapınar, Erdal; Karapinar,E.; Roldán Lpez De Hierro,A.F.; MathematicsWe show that the main result in the work by Mutlu et al. is not true. We explain point by point some of its main mistakes and we propose an alternative version to smooth away the defects of it. © 2015 Hamed H. Alsulami et al.Editorial Citation Count: 0New contribution to the advancement of fixed point theory, equilibrium problems, and optimization problems 2014(Hindawi Publishing Corporation, 2015) Karapınar, Erdal; Karapinar,E.; Lin,L.-J.; Lee,G.M.; Mathematics[No abstract available]Article Citation Count: 12A note on 'n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces'(2013) Karapınar, Erdal; Roldán,A.; MathematicsIn this note, we show that multidimensional fixed point theorems established in the recent report [M. Ertürk and V. Karakaya, n-tuplet fixed point theorems for contractive type mappings in partially orderedmetric spaces, Journal of Inequalities and Applications 2013, 2013:196] have gaps. Furthermore, the results of the mentioned paper can be reduced to unidimensional (existing) fixed point theorems. ©2013 Karapinar and Roldán; licensee Springer.Article Citation Count: 68A note on common fixed point theorems in partial metric spaces(University of Miskolc, 2011) Karapınar, Erdal; MathematicsIn this manuscript, we consider the notion of generalized Sehgal contraction condition in a partial metric space. For the pair of two self mappings (S, T) which satisfies Sehgal contraction condition, we obtain a unique common fixed point. © 2011 Miskolc University Press.Conference Object Citation Count: 1On (α, ψ) contractions of integral type on generalized metric spaces(Springer International Publishing, 2015) Karapınar, Erdal; MathematicsIn this paper, we investigate the existence and uniqueness of fixed points of (α,ψ)-contractive mappings of integral type in complete generalized metric spaces, introduced by Branciari. Our results generalize and improve several results in literature. © 2015 Springer International Publishing Switzerland.Article Citation Count: 22On Ekeland's variational principle in partial metric spaces(Natural Sciences Publishing Co., 2015) Karapınar, Erdal; Karapinar,E.; Vetro,C.; MathematicsIn this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of partial metric spaces. As consequences of our results, we obtain some fixed point theorems of Caristi and Clarke types. © 2015 NSP.Book Part Citation Count: 2On the approximation of solutions to a fixed point problem with inequality constraints in a Banach space partially ordered by a cone(Springer Singapore, 2017) Karapınar, Erdal; Karapinar,E.; Samet,B.; MathematicsLet E be a Banach space with a cone P. Let T, ϕi: E → E (i = 1, 2) be three given operators. We address the following question: Find x ε E such that where ≤P is the partial order on E induced by the cone P, and 0E is the zero vector of E. We obtain sufficient conditions for the existence and uniqueness of solutions to this problem. We present an iterative algorithm to approximate the solution. The error estimates as well as results concerning the data dependence, well-posedness, limit shadowing property, and sequences of operators are provided. Some interesting consequences are deduced from our main results. © Springer Nature Singapore Pte Ltd. 2017. All rights reserved.Article Citation Count: 6On α*-ψ-contractive multi-valued operators in b-metric spaces and applications(Natural Sciences Publishing Co., 2015) Karapınar, Erdal; Ilea,V.; Karapinar,E.; Mleşniţe,O.; MathematicsIn this paper, we will prove some existence and uniqueness theorems for α*-ψ contractive type operators defined over bmetric spaces. In particular, we will provide results related to Ulam-Hyers stability, well-posedness and limit shadowing. The theorems presented will extend, generalize or unify several statements currently exist in the literature on those topics.We will also give examples to illustrate the applications our results. © 2015 NSP Natural Sciences Publishing Cor.Book Part Citation Count: 14A short survey on dislocated metric spaces via fixed-point theory(Springer Singapore, 2017) Karapınar, Erdal; MathematicsIn 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 Count: 12Some applications of Caristi’s fixed point theorem in metric spaces(Springer International Publishing, 2016) Karapınar, Erdal; Karapinar,E.; Khandani,H.; MathematicsIn this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce the idea that many of known fixed point theorems can easily be derived from the Caristi theorem. Finally, the existence of bounded solutions of a functional equation is studied. © 2016 Khojasteh et al.