Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 16764, 9 pages
doi:10.1155/JIA/2006/16764
The system of generalized set-valued equilibrium problems
College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
Received 14 September 2004; Revised 11 November 2004; Accepted 18 November 2004
Copyright © 2006 Jian-Wen Peng. 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 new and interesting model of system of generalized set-valued equilibrium problems which generalizes and unifies the system of set-valued equilibrium problems, the system of generalized implicit vector variational inequalities, the system of generalized vector and vector-like variational inequalities introduced by Ansari et al. (2002), the system of generalized vector variational inequalities presented by Allevi et al. (2001), the system of vector equilibrium problems and the system of vector variational inequalities given by Ansari et al. (2000), the system of scalar variational inequalities presented by Ansari Yao (1999, 2000), Bianchi (1993), Cohen and Caplis (1988), Konnov (2001), and Pang (1985), the system of Ky-Fan variational inequalities proposed bt Deguire et al. (1999) as well as a variety of equilibrium problems in the literature. Several existence results of a solution for the system of generalized set-valued equilibrium problems will be shown.