Approximation Solvability of System of Generalized Mixed ImplicitEquilibrium Problems in Banach Spaces

A new system of generalized mixed implicit equilibrium problems involving non-monotone set-valued mappings 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.Further,by using the notion of the Yosida approximation,a system of generalized Wiener-Hopf equations problems is considered and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved.By using a fixed point formulation of the system of generalized Wiener-Hopf equations problems,a new iterative algorithm for solving the system of generalized mixed implicit 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.