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

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 uniformly quasi-𝜙-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.

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