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Citation - WoS: 70
Citation - Scopus: 69
Best Proximity Points of Cyclic Mappings
(Pergamon-elsevier Science Ltd, 2012) Karapinar, Erdal
In 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.
Citation - WoS: 46
Citation - Scopus: 43
Cyclic Contractions and Fixed Point Theorems
(Univ Nis, Fac Sci Math, 2012) Karapinar, Erdal; Erhan, Inci M.
In this manuscript, the existence and uniqueness of fixed points of a class of cyclic operators defined on a closed subset of a Banach space is discussed. Fixed point theorems for some contractions from this class are introduced and illustrative examples are given.