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The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f-projection method for finding a common element of the fixed point set for a countable family of uniformlyquasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixedequilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Kleeproperty. Furthermore, we prove that our new iterative scheme converges strongly to a common elementof the aforementioned sets. The results presented in this paper improve and extend important recentresults in the literature

abstract and applied analysis

Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems