Algorithm of Solutions for Solving Generalized Mixed Implicit Equilibrium Problems.

A new system of generalized mixed implicit equilibrium problems is introduced and studied in real reflexive Banach space. A system of generalized equation problems is considered and its equivalence with the system of generalized mixed implicit equilibrium problems is shown. The iterative algorithm of the solutions is constructed and analyzed through a fixed point formulation of the generalized equation problems. The existence of solutions for the equilibrium problems is obtained. The convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. The results in this paper extend and improve some known results in the literature.