Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 82695, 16 pages
doi:10.1155/JIA/2006/82695

Iterative algorithm for solving mixed quasi-variational-like inequalities with skew-symmetric terms in Banach spaces

Lu-Chuan Ceng,1 Qamrul Hasan Ansari,2,3 and Jen-Chih Yao4

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
3Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, P.O. Box 1169, Dhahran 31261, Saudi Arabia
4Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan

Received 1 April 2006; Accepted 28 May 2006

Copyright © 2006 Lu-Chuan Ceng 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 develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces. We use Fan-KKM lemma and concept of η-cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalities with skew-symmetric terms. Furthermore, we derive the posteriori error estimates for approximate solutions under quite mild conditions.