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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 681348, 19 pages
http://dx.doi.org/10.1155/2012/681348
Research Article

Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators

1Mathematics Institute, African University of Science and Technology, Abuja, Nigeria
2Department of Mathematics, Gaston Berger University, Saint Louis, Senegal

Received 20 November 2011; Accepted 19 January 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 C. E. Chidume and N. Djitté. 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

An iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation where A is a bounded m-accretive operator on certain real Banach spaces E that include spaces The iteration process does not involve the computation of the resolvent at any step of the process and does not involve the projection of an initial vector onto the intersection of two convex subsets of E, setbacks associated with the classical proximal point algorithm of Martinet 1970, Rockafellar 1976 and its modifications by various authors for approximating of a solution of this equation. The ideas of the iteration process are applied to approximate fixed points of uniformly continuous pseudocontractive maps.