Existence Of Solutions For Some Generalized Equilibrium Problems With Set-valued Mappings

The equilibrium problem provides a unified model for the study of fixed point problems,variational inequality problems,saddle point problems,Nash equilibrium problems,complementary problems and optimization problems,etc.In social and economic life,they often consider not one but multiple goals,and some are even collective values,when people face many practical decision making problems.Therefore,it is very necessary to study the vector set-valued equalization problem.In this thesis,we study the existence theorems of solutions for several types of generalized vector set-valued equilibrium problems.Firstly,by virtue of well-known Fan-KKM theorem,the existence results of solutions for the scalar set-valued equilibrium problem are obtained.Then,the existence theorems of solutions to the vector set-valued equalization problem are obtained by using the linear scalar function and the nonlinear scalar function respectively.Finally,the obtained results of the existence of the vector set-valued equilibrium problem are applied to the vector saddle point problem and the vector Nash equilibrium problem,and the corresponding existence results are obtained.