A Maximal Element Theorem in FWC-Spaces and Its Applications. (20th March 2014)

• Record Type: Journal Article
• Authors: Lu, Haishu; Hu, Qingwen; Miao, Yulin
• Other Names: Al-Sawalha M. M. S. Academic Editor.; Beg I. Academic Editor.; Cheng Y. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-03-20
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/890696
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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.