Abstract and Applied Analysis
Volume 2012 (2012), Article ID 768272, 10 pages
http://dx.doi.org/10.1155/2012/768272
Research Article

Iterative Algorithms for General Multivalued Variational Inequalities

Yonghong Yao,1 Muhammad Aslam Noor,2,3 Yeong-Cheng Liou,4 and Shin Min Kang5

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Mathematics Department, College of Science, King Saud University, Riyadh 1145, Saudi Arabia
3Mathematics Department, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan
4Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
5Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 21 October 2011; Accepted 1 November 2011

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Yonghong Yao et al. 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 and study some new classes of variational inequalities and the Wiener-Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and analyze some iterative methods for solving the general multivalued variational in equalities in conjunction with nonexpansive mappings. We prove a strong convergence result for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general multivalued variational inequalities under some mild conditions. Several special cases are also discussed.