Convergence And Iterative Algorithms For Systems Of Generalized Mixed Equilibrium Problems

Variational inequality has a wide-ranging applied background, projection method is considered as a kind of special methods to solve the problem. Equilibrium problem as a promotion of variational inequalities, plays an important role in engineering science and mechanics. Fixed point theory is an useful tool of solving equilibrium problem. Convergence and iterative algorithms for systems of generalized mixed equilibrium problems in Banach space are studied in this paper, at the same time, convergence and the generalized f? projection algorithm of generalized mixed variational inequalities in Hilbert space are also considered.The main results of this thesis may be summarized as follows:In chapter 2, the iterative algorithms for system of generalized mixed equilibrium problems in Banach space are studied. In the two parts, the iterative algorithms for the system of two generalized mixed equilibrium problems and system of multi-generalized mixed equilibrium problems are introduced. And the strong convergence theorems of iterative algorithm for finding a common element of the fixed point set of relatively nonexpansive mappings and the solution set of system of generalized mixed equilibrium problems in Banach space under some suitable conditions are proved. The results correct previous result of pertinent literature.In chapter 3, the generalized f? projection algorithm of generalized mixed variational inequalities in Hilbert space is studied. In this part, the property of f? projection operator is used to provide a new iterative algorithm to study the convergence of the iterative algorithm. the result is that the iterative algorithm converges to the solution of generalized mixed variational inequalities.