Maximal Element Principles on Generalized Convex Spaces and Their Applications *

Some existence theorems of maximal elements involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are first proved in generalized convex spaces. Next, as applications, some new coincidence theorems, fixed point theorems, minimax inequalities, section theorems and existence theorems of solutions for quasi-equilibrium problems are given in generalized convex spaces. Finally, noncompact infinite optimization problems and equilibrium existence problems for constrained games are also discussed. These theorems improve and generalize many important known results in recent literature.