Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 561573, 12 pages
doi:10.1155/2011/561573
Research Article

Systems of Generalized Quasivariational Inclusion Problems with Applications in LΓ-Spaces

Ming-ge Yang,1,2 Jiu-ping Xu,3 and Nan-jing Huang1,3

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, China
3College of Business and Management, Sichuan University, Chengdu, Sichuan 610064, China

Received 27 September 2010; Accepted 22 October 2010

Academic Editor: Yeol J. E. Cho

Copyright © 2011 Ming-ge Yang 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 first prove that the product of a family of LΓ-spaces is also an LΓ-space. Then, by using a Himmelberg type fixed point theorem in LΓ-spaces, we establish existence theorems of solutions for systems of generalized quasivariational inclusion problems, systems of variational equations, and systems of generalized quasiequilibrium problems in LΓ-spaces. Applications of the existence theorem of solutions for systems of generalized quasiequilibrium problems to optimization problems are given in LΓ-spaces.