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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 264909, 9 pages
http://dx.doi.org/10.1155/2014/264909
Research Article

A New Iterative Scheme of Modified Mann Iteration in Banach Space

College of Applied Mathematics, Chengdu University of Information Technology, No. 24, Block 1, Xuefu Road, Chengdu 610225, China

Received 5 October 2013; Revised 28 December 2013; Accepted 29 December 2013; Published 11 February 2014

Academic Editor: Sehie Park

Copyright © 2014 Jinzuo Chen et al. 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

We introduce the modified iterations of Mann's type for nonexpansive mappings and asymptotically nonexpansive mappings to have the strong convergence in a uniformly convex Banach space. We study approximation of common fixed point of asymptotically nonexpansive mappings in Banach space by using a new iterative scheme. Applications to the accretive operators are also included.