New Iterative Algorithm for Solving a System of Generalized Mixed Implicit Equilibrium Problems in Banach Spaces

Abstract

A new system of generalized mixed implicity equilibrium problems is introduced and studied in real Banach spaces. The notion of the Yosida approximation introduced by Moudafi in Hilbert spaces is first generalized to reflexive Banach spaces. By using the notion of the Yosida approximation, a system of generalized equation problems is considered and its equivalence with the system of generalized mixed implicity equilibrium problems is also proved. By using the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new and unify and generalize some recent results in this field.