Strong convergence theorems for countable families of uniformly quasi-\(\phi\)-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems (Q638138)

Summary: 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-\(\phi\)-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.