[[alternative]]Fixed Point Theorems、KKM Theorems and its Applications

[[abstract]]The purpose of this paper is to study the fixed point theory and the KKM theory , we get some fixed point theorems and generalized KKM theorems. As applications, we use the above results to related topics, for examples, the matching theorems, the existence theorems of quasi-equilibrium, quasi-variational inequalities. This paper contains three chapters. In the first chapter, we discuss some fixed point theorems and coincidence theorems about inward contractive functions and inward nonexpansive functions. In second chapter, we introduce some conceptions of non-convexities, study their properties, and apply these properties to get some generalized KKM theorems, the matching theorems, and the existence theorems of quasi-equilibrium. In this chapter, we also introduce a new family of functions, Q(X,Y), we research its properties and get some fixed point theorems about this family. In the last chapter, we study the properties of the family of approachable functions in uniform spaces. By using these properties, we attain some fixed point theorems and coincidence theorems. The results of this paper actually extend many results of authors as in the references.