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Abstract and Applied Analysis
Volume 2014, Article ID 580621, 7 pages
http://dx.doi.org/10.1155/2014/580621
Research Article

Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

1Department of Mathematics, Shawnee State University, Portsmouth, OH 45662, USA
2College of Mathematics and Computer, Hebei University, Baoding, Hebei 071002, China

Received 15 January 2014; Accepted 14 March 2014; Published 9 April 2014

Academic Editor: Chong Li

Copyright © 2014 Jinlu Li 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 apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.