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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: 44Best Proximity Points of Kannan Type Cyclic Weak Ø-Contractions in Ordered Metric Spaces(Ovidius University, 2012) Karapinar,E.In 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 - Scopus: 13Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces(2013) Aydi,H.; Karapinar,E.; Mustafa,Z.In this paper, we prove tripled coincidence and common fixed point theorems for F : X × X × X → X and g : X → X satisfying almost generalized contractions in partially orderedmetric spaces. The presented results generalize the theoremof Berinde and Borcut [Tripled fixed point theorems for contractive typemappings in partially orderedmetric spaces, Nonlinear Anal. 74 (15) (2011) 4889-4897]. Also, some examples are presented.Article Citation - Scopus: 29Fixed Point Theorem on Partial Metric Spaces Involving Rational Expressions(University of Miskolc, 2013) Karapinar,E.; Shatanawi,W.; Tas,K.We 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 - WoS: 11Citation - Scopus: 7Edelstein Type Fixed Point Theorems(Tusi Mathematical Research Group, 2011) Karapinar,E.; Karapınar, Erdal; Karapınar, Erdal; Mathematics; 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 - Scopus: 71A Note on Common Fixed Point Theorems in Partial Metric Spaces(University of Miskolc, 2011) Karapinar,E.In 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.Editorial New Contribution To the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems 2014(Hindawi Publishing Corporation, 2015) Du,W.-S.; Karapinar,E.; Lin,L.-J.; Lee,G.M.[No abstract available]Article Citation - Scopus: 105Solution of fractional differential equations via coupled fixed point(Texas State University - San Marcos, 2015) Afshari,H.; Kalantari,S.; Karapinar,E.In this article, we investigate the existence and uniqueness of a solution for the fractional differential equation by introducing some new coupled fixed point theorems for the class of mixed monotone operators with pertur-bations in the context of partially ordered complete metric space. © 2015 Texas State University - San Marcos.Article Citation - Scopus: 54Fixed Point Results for Generalized Α-Ʋ in Metric-Like Spaces and Applications(Texas State University - San Marcos, 2015) Aydi,H.; Karapinar,E.In this article, we introduce the concept of generalized α- ʋ -con- traction in the context of metric-like spaces and establish some related fixed point theorems. As consequences, we obtain some known fxed point results in the literature. Some examples and an application on two-point boundary value problems for second order differential equation are also considered. © 2015 Texas State University - San Marcos.
