Journal of Applied Mathematics
Volume 2012 (2012), Article ID 504503, 19 pages
http://dx.doi.org/10.1155/2012/504503
Research Article

An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces

H. Zegeye1 and N. Shahzad2

1Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone, Botswana
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 24 February 2012; Accepted 5 April 2012

Academic Editor: Yonghong Yao

Copyright © 2012 H. Zegeye and N. Shahzad. 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 introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.