Abstract and Applied Analysis
Volume 2010 (2010), Article ID 285376, 14 pages
doi:10.1155/2010/285376
Research Article

Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces

Yekini Shehu1 and Jerry N. Ezeora2

1Department of Mathematics, University of Nigeria, Nsukka, Nigeria
2Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

Received 29 January 2010; Revised 19 June 2010; Accepted 27 June 2010

Academic Editor: S. Reich

Copyright © 2010 Yekini Shehu and Jerry N. Ezeora. 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 E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping j, path convergence is proved for a nonexpansive mapping T:K→K. As an application, we prove strong convergence theorem for common zeroes of a finite family of m-accretive mappings of K to E. As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from K to E under certain mild conditions.