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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 602582, 6 pages
http://dx.doi.org/10.1155/2013/602582
Research Article

An Implicit Iteration Process for Common Fixed Points of Two Infinite Families of Asymptotically Nonexpansive Mappings in Banach Spaces

College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

Received 30 October 2012; Accepted 18 January 2013

Academic Editor: Jinde Cao

Copyright © 2013 Wei-Qi Deng and Peng Bai. 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

Let be a nonempty, closed, and convex subset of a real uniformly convex Banach space . Let and be two infinite families of asymptotically nonexpansive mappings from to itself with . For an arbitrary initial point , is defined as follows: , , , where and with and satisfying the positive integer equation: , ; and are two countable subsets of and respectively; , , , , , and are sequences in for some , satisfying and . Under some suitable conditions, a strong convergence theorem for common fixed points of the mappings and is obtained. The results extend those of the authors whose related researches are restricted to the situation of finite families of asymptotically nonexpansive mappings.