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The Scientific World Journal
Volume 2014, Article ID 890696, 18 pages
Research Article

A Maximal Element Theorem in FWC-Spaces and Its Applications

1School of Business, Jiangsu University of Technology, Changzhou, Jiangsu 213001, China
2Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA

Received 24 August 2013; Accepted 5 December 2013; Published 20 March 2014

Academic Editors: M. M. S. Al-Sawalha, I. Beg, and Y. Cheng

Copyright © 2014 Haishu Lu 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.


A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature.