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

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.