KKM Type Theorems, Equilibrium Problems With Lower And Upper Bounds, Maximal Elements, Coincidence Theorems With Their Applications In The G-convex Spaces

The KKM principle and equilibrium problem theory are very useful tools for studied various nonlinear problems from natural and social sciences. Its applications are so broad that these theories and applications are in their rapid developing stages. Undoubtedly, more and more new and exciting results will be found in the near future.In this paper, the KKM principle and its variation are studied in the G -convex spaces and the product space of the G -convex spaces. As application, some new minimax inequalities are obtained. Some existence theorems of equilibrium points for equilibrium problems with lower and upper bounds are established in the G-convex spaces. Some new existence theorems of maximal elements and coincidence theorems are proved in the G-convex spaces.The organization of this paper as follow:In Chapter 1, some new KKM type theorems are established in the product space of the G-convex spaces. KKM type theorems and their variant forms are also studied, some applications to minimax inequalities are given.In Chapter 2, some equilibrium theorems for equilibrium problems with lower and upper bounds are established in the G-convex spaces.In Chapter 3, together with Ding Xie-ping and Fang Min, we proved some new existence theorems of maximal elements and coincidence theorems involving better admissible mappings under noncompact setting of G-convex spaces.