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Article Citation - Scopus: 7Fixed Point Theory for Cyclic Generalized (φ-Φ) Mappings(Springer-Verlag Italia s.r.l., 2013) Karapinar,E.; Moradi,S.Fixed 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 - Scopus: 16A gap in the paper a note on cone metric fixed point theory and its equivalence(Gazi Universitesi, 2011) Abdeljawad,T.; Karapinar,E.There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.Article On Pairs of ℓ-Köthe Spaces(Hacettepe University, 2010) Karapinar,E.Let ℓ be a Banach sequence space with a monotone norm {double pipe}· {double pipe} ℓ, in which the canonical system (ei) is a normalized unconditional basis. Let a = (ai), ai → ∞, λ = (λi) be sequences of positive numbers. We study the problem on isomorphic classification of pairs F = (Kℓ(exp(-1/p ai)),Kℓ(exp (-1/p ai + λi))). For this purpose, we consider the sequence of so-called m-rectangle characteristics μF m. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type ℓ-power series spaces. By using analytic scale and a modification of some invariants (modified compound invariants) it is proven that m-rectangular characteristics are invariant on the class of such pairs. Deriving the characteristic β̃ from the characteristic β, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121-142, 1997).Article Citation - Scopus: 10Note on “modified Α-Ψ Mappings With Applications”(Chiang Mai University, 2015) Berzig,M.; Karapinar,E.In this short paper, we unexpectedly notice that the modified version of α-ψ-contractivemappings, suggested by Salimi et al. [Modified α-ψ-contractive mappings with applications, Fixed Point Theory and Applications 2013, 2013:151] is not a real generalization. © 2015 by the Mathematical Association of Thailand. All rights reserved.Book Part Citation - Scopus: 14A Short Survey on Dislocated Metric Spaces Via Fixed-Point Theory(Springer Singapore, 2017) Karapinar,E.In 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 - Scopus: 12Different Types Meir-Keeler Contractions on Partial Metric Spaces(2012) Erhan,I.M.; Karapinar,E.; Türkoǧlu,D.In this manuscript, Meir-Keeler contractions on partial metric spaces are introduced. It is shown that if a self-mapping T on a complete partial metric spaces is a Meir-Keeler contraction, then T has a unique fixed point. © 2012 EUDOXUS PRESS, LLC.Book Citation - Scopus: 113Fixed Point Theory in Metric Type Spaces(Springer International Publishing, 2016) Agarwal,R.P.; Karapinar,E.; O’regan,D.; Roldán-López-De-Hierro,A.F.Written 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 - Scopus: 62Weak ø-Contraction on partial metric spaces(2012) Karapinar,E.In this manuscript, the notion of weak ø-contraction is considered on partial metric space. It is shown that a self mapping T on a complete partial metric space X has a fixed point if they satisfied weak ø-contraction. © 2012 EUDOXUS PR20E6SS, LLC.Article Citation - Scopus: 16Fixed Point Theory for the Α-Admissible Meir-Keeler Type Set Contractions Having Kkm* Property on Almost Convex Sets(Natural Sciences Publishing, 2017) Chen,C.-M.; Abkar,A.; Ghods,S.; Karapinar,E.The 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.Article Citation - Scopus: 75Fixed Points of Generalized Α-Admissible Contractions on B-Metric Spaces With an Application To Boundary Value Problems(Yokohama Publications, 2016) Aksoy,Ü.; Karapinar,E.; Erhan,I.M.A general class of α-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations. © 2016.
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