Existence and algorithms for solutions to a new System of Generalized Mixed Equilibrium Problems in Banach spaces

摘要

In this paper, we introduce and study a new System of Generalized Mixed Equilibrium Problems (for short, SGMEP) involving set-valued mappings in Banach spaces. First, the existence and uniqueness of solutions to a new System of Auxiliary Generalized Mixed Equilibrium Problems (for short, SAGMEP) is proved under quite mild conditions. Next, by using the auxiliary principle technique, new iterative algorithms for solving the system of generalized mixed equilibrium problems are suggested and analyzed. The results presented here are new and generalize some recent results in this field.