Iterative Algorithm For Solving Variational Inclusions And Equilibrium Problems

This paper mainly further studies iterative algorithm of solutions for the system of variational inclusions, the system of equilibrium problems, it also improves and generalizes some known results in recent literatures. First, the background of variational inclusions and equilibrium problems theory, recent situation of research are introduced. In the second chapter, a new system of generalized mixed quasi-variational-like inclusions with (H,η)-accretive operators are introduced and studied in Banach spaces. By using the resolvent technique for the general (H,η)-accretive operators, we prove the existence of solutions and the convergence of a new iterative algorithm for this system of generalized mixed quasi-variational-like inclusions in Banach spaces. In the third chapter, a new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators are introduced and studied. By using the resolvent technique, we prove the existence of solutions for this system of generalized mixed quasi-variational inclusions. We also prove the convergence of a new iterative algorithm approximating the solution for this system of generalized mixed quasi-variational inclusions. In the forth chapter, we introduce and study a new system of generalized mixed implicit equilibrium problems in reflexive Banach spaces. This equilibrium problem includes many equilibrium problems, variational inequality as special cases. By using a fixed point formulation of the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicit equilibrium problems are suggested and analyzed. And we also prove the convergence of the iterative sequences generated by the algorithm under suitable conditions. The results presented in this paper extend and improve many corresponding results in the literature.