A maximal element theorem in FWC-spaces and its applications.
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.
School of Business, Jiangsu University of Technology, Changzhou, Jiangsu 213001, China.
Haishu
0000-0002-3271-6105
H
Lu
Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA.
Qingwen
Q
Hu
School of Business, Jiangsu University of Technology, Changzhou, Jiangsu 213001, China.
Yulin
Y
Miao
D000465:Algorithms; D003198:Computer Simulation; D055641:Mathematical Concepts; D008962:Models, Theoretical; D015203:Reproducibility of Results