KKM Theorem And It's Applications In G-convex Space

Since 1960s, Lions,Stampacchia Browder, Ky Fan put forward and established the basic theory of variational inequality, after many mathematicians'outstanding work, variational inequality and related theory and applications have made important progress.Variational inequality and related KKM theory, Ky Fan minimax value , Ky Fan minimax inequality and the complementarity problem are the important part of the nonlinear analysis, it has extensive relation with mechanics, differential equations,the theory of control, the economic mathematics, optimal problem, nonlinear programming theory and has important applications.Along with the further research on variational inequality theory, in 1996, Kim and Park introduced the concept of G-Convex Space and did many important works, the main purpose of this paper is to study the KKM theory and it's applications in G-Convex Space.The paper consists of four parts.The main results of this paper are summarized as following:In the first chapter, we simply narrate the development of the KKM theory home and abroad in the preface.And the main content that we will discuss,background and significance are introduced.In the second chapter, some definitions,lemmas and related knowledge used in the article are introduced in the preparation. In the third chapter, variational inequalities and the fixed point theorems are discussed in G-Convex Space, and the equivalent forms of fixed point theorems are given.In the last chapter, The KKM type theorems are established and as applications, the new matching theorems, section theorems and minimax theorems and some related results. are established.