Journal of Applied Mathematics
Volume 2012 (2012), Article ID 912050, 14 pages
http://dx.doi.org/10.1155/2012/912050
Research Article

A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically 𝜙 -Strongly Pseudocontractive Mappings

Luigi Muglia1 and Yonghong Yao2

1Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende, Italy
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 20 January 2012; Accepted 15 February 2012

Academic Editor: Giuseppe Marino

Copyright © 2012 Luigi Muglia and Yonghong Yao. 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

In this paper we prove the equivalence and the strong convergence of an explicit Mann iterative process and a modified implicit iterative process for asymptotically 𝜙 -strongly pseudocontractive mappings in a uniformly smooth Banach space.