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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: 142Citation - Scopus: 137Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces(Springer international Publishing Ag, 2011) Karapinar, ErdalIn this article, lower semi-continuous maps are used to generalize Cristi-Kirk's fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces. Some more general results are also obtained in partial metric spaces. 2000 Mathematics Subject Classification 47H10,54H25Article Citation - WoS: 70Citation - Scopus: 68Best Proximity Points of Cyclic Mappings(Pergamon-elsevier Science Ltd, 2012) Karapinar, ErdalIn this this manuscript, we proved that the existence of best proximity points for the cyclic operators T defined on a union of subsets A, B of a uniformly convex Banach space X with T (A) subset of B, T(B) subset of A and satisfying the condition parallel to Tx - Yy parallel to <= alpha/3[parallel to x-y parallel to + parallel to Tx - x parallel to + parallel to Ty - y parallel to] + (1 - alpha)diam(A, B) for alpha is an element of (0, 1) and for all x is an element of A, for all y is an element of B, where diam(A, B) = inf{parallel to x - y parallel to : x is an element of A, y is an element of B}. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 173Fixed Point Theory for Cyclic Weak Φ-Contraction(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Karapınar, Erdal; Karapınar, Erdal; Mathematics; MathematicsIn this manuscript, the notion of cyclic weak phi-contraction is considered. It is shown that a self-mapping T on a complete metric space X has a fixed point if it satisfied cyclic weak phi-contraction. (C) 2010 Elsevier Ltd. All rights reserved.
