Existence and Algorithm of Solutions for a System of Generalized Mixed Equilibrium Problems in Real Banach Spaces

A new system of generalized mixed equilibrium problems is studied in Banach spaces. First, a system of auxiliary generalized mixed equilibrium problems is introduced, and its existence and uniqueness are also proved. Next, by applying the system of auxiliary generalized mixed equilibrium problems, an iterative algorithm for solving the system of generalized mixed equilibrium problems is constructed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results improve and generalize some recent known results in the literature.