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In this paper, we propose and analyze an explicit type algorithm for finding a common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two countable families of total quasi-φ-asymptotically nonexpansive mappings in a Banach space E. As an application of our result, we suggest a framework for finding a common solution of a finite family of generalized equilibrium problems and common zeros of two finite families of maximal monotone operators on E.

Mosco convergence results for common fixed point problems and generalized equilibrium problems in Banach spaces