Abstract and Applied Analysis
Volume 2012 (2012), Article ID 470354, 25 pages
http://dx.doi.org/10.1155/2012/470354
Research Article

Viscosity Iterative Schemes for Finding Split Common Solutions of Variational Inequalities and Fixed Point Problems

Zhenhua He1 and Wei-Shih Du2

1Department of Mathematics, Honghe University, Yunnan 661100, China
2Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan

Received 12 August 2012; Accepted 25 September 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Zhenhua He and Wei-Shih Du. 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 some new iterative schemes based on viscosity approximation method for finding a split common element of the solution set of a pair of simultaneous variational inequalities for inverse strongly monotone mappings in real Hilbert spaces with a family of infinitely nonexpansive mappings. Some strong convergence theorems are also given. Our results generalize and improve some well-known results in the literature and references therein.