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In this paper, a new modified Ishikawa iterative algorithm with errors by a shrinking projection method for generalized mixed equilibrium problems and a countable family of uniformly Bregman totally quasi- D-asymptotically nonexpansive mappings is introduced and investigated in the framework of a real Banach space. Strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field. [ABSTRACT FROM AUTHOR]

In this paper, we investigate common solutions to a family of mixed equilibrium problems with a relaxed η- α-monotone mapping and a nonlinear operator equation involving an infinite family of asymptotically quasi- ϕ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space. These results extend many important recent ones in the literature. [ABSTRACT FROM AUTHOR]