Abstract
In this paper, we introduce an iterative scheme by the modified Halpern- Mann-type for total quasi-ϕ-asymptotically nonexpansive semi-groups and prove the strong convergence theorem using our new iterative process which converges strongly to a common element of the set of common fixed points for total quasi-ϕ-asymptotically nonexpansive semi-groups and the set of solutions of generalized mixed equilibrium problem in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property using the properties of the generalized f-projection operator. Our results extend and improve the corresponding recent results in the literature.
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