Abstract and Applied Analysis
Volume 2010 (2010), Article ID 301305, 18 pages
doi:10.1155/2010/301305
Research Article

Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications

Somyot Plubtieng1,2 and Wanna Sriprad1,2

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 19 September 2010; Accepted 28 October 2010

Academic Editor: W. A. Kirk

Copyright © 2010 Somyot Plubtieng and Wanna Sriprad. 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 present two iterative schemes with errors which are proved to be strongly convergent to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space. Using the result we consider strong convergence theorems for variational inequalities and equilibrium problems in a real Hilbert space and strong convergence theorems for maximal monotone operators in a real uniformly smooth and uniformly convex Banach space.