The Study And Applications Of KKM Theorems And Multivalued General Mixed Implicit Equilibrium-like Problems

KKM theorems and the corresponding applications in different spaces are proved in the first two chapters of this paper.The third chapter independently studies the multivalued general mixed implicit equilibrium-like problems.The main content of the paper is demonstrated as following:Firstly,the background and current state of KKM theory and variational inequality theory are discussed.Secondly,using the connectedness of set and a characteristic property in FCspaces, a parametric type of KKM theorem is established in noncompact FC-spaces by introducing a linear ordered space.The result is applied to get noncompact minimax inequalities,saddle point theorem and section theorem.Thirdly,a new class of generalized better admissible set-valued mappings is introduced and a coincidence theorem for generalized better admissible set-valued in abstract convex topological spaces is obtained.The result is applied to get a KKM type theorem and maximal element theorem.Finally,the multivalued general mixed implicit equilibrium-like problems are introduced and studied.To solve these problems,a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique.The convergence of the suggested algorithm is also proved in some conditions.