Abstract and Applied Analysis
Volume 2011 (2011), Article ID 251612, 19 pages
doi:10.1155/2011/251612
Research Article

Strong Convergence Theorems for Families of Weak Relatively Nonexpansive Mappings

Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

Received 30 September 2010; Revised 25 November 2010; Accepted 15 February 2011

Academic Editor: Jean Pierre Gossez

Copyright © 2011 Yekini Shehu. 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 construct a new Halpern type iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalized 𝑓 -projection operator. Using this result, we discuss strong convergence theorem concerning general 𝐻 -monotone mappings. Our results extend many known recent results in the literature.