Abstract and Applied Analysis
Volume 2012 (2012), Article ID 850104, 19 pages
http://dx.doi.org/10.1155/2012/850104
Research Article

On the Convergence of Mann and Ishikawa Iterative Processes for Asymptotically 𝜙 -Strongly Pseudocontractive Mappings

Xuewu Wang,1 Giuseppe Marino,2 and Luigi Muglia2

1College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, China
2Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende, Italy

Received 13 October 2011; Accepted 29 December 2011

Academic Editor: Ngai-Ching Wong

Copyright © 2012 Xuewu Wang 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 prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptotically 𝜙 -strongly pseudocontractive mappings in a uniformly smooth Banach space.