Fixed Point Theory And KKM Theory And Its Application

In this paper, we mainly study the common fixed point theory in uniformly convex metric spaces, the T-KKM theory in FWC-spaces and its applications.The paper contains four parts as following:The chapter one introduce the backgrounds of the common fixed point theory , KKM theory,and significance of study in this paper.In chapter two,we discussed the existence and uniqueness of common fixed point theorems in uniformly convex metric spaces by using weak compatible mapping pairs and convex modulus, Some new common fixed point theorems are given,which largely improve and extend some relative results that have been published recently in uniformly convex metric spaces.In chapter three,we introduce a class of generalized T-KKM mapping in the FWC-spaces and established some nonempty compact closed valued mappings T-KKM type theorems.As application,Fan-Browder fixed point theorem,Ky Fan sec-tion theorem and existence theorem of solutions for the generalized vector equilib-rium problem are obtained in FWC-spaces.In chapter four,we introduce eight new systems of generalized vector quasi-equilibrium problems and discuss their the existence of solutions in FWC-spaces.