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Article Citation - WoS: 70Citation - Scopus: 69Best 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: 21Citation - Scopus: 18On a Cyclic Jungck Modified ts-iterative Procedure With Application Examples(Elsevier Science inc, 2014) De la Sen, M.; Karapinar, E.; Alemdaroğlu Temel, Mine; Alemdaroğlu Temel, MineThis article investigates some convergence properties of quasi-cyclic and cyclic Jungck modified TS-iterative schemes in complete metric spaces and Banach spaces. The uniqueness of the best proximity points is investigated. It is basically assumed that one of the self-mappings is asymptotically nonexpansive while the other is asymptotically contractive with several particular cases. Some application examples are also discussed. (C) 2014 Elsevier Inc. All rights reserved.
