A Maximal Element Theorem inFWC-Spaces and Its Applications
Haishu Lu, Qingwen Hu, Yulin Miao · The Scientific World JOURNAL · 2014
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.