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Abstract and Applied Analysis
Volume 2013, Article ID 183174, 14 pages
http://dx.doi.org/10.1155/2013/183174
Research Article

On Best Proximity Point Theorems and Fixed Point Theorems for -Cyclic Hybrid Self-Mappings in Banach Spaces

Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus of Leioa (Bizkaia), P.O. Box 644 Bilbao, 48090, Spain

Received 26 December 2012; Accepted 12 February 2013

Academic Editor: Yisheng Song

Copyright © 2013 M. De la Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent -hybrid -cyclic self-mappings relative to a Bregman distance , associated with a Gâteaux differentiable proper strictly convex function in a smooth Banach space, where the real functions and quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping. Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.