An iterative method for total quasi-ϕ-asymptotically nonexpansive semi-groups and generalized mixed equilibrium problems in Banach spaces

Jae Ug Jeong and Soo Hwan Kim

Applied Mathematics and Computation, 2015, vol. 254, issue C, 39-48

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.

Keywords: Total quasi-ϕ-asymptotically nonexpansive semi-group; Quasi-ϕ-asymptotically nonexpansive semi-group; Quasi-ϕ-nonexpansive semi-group; Generalized mixed equilibrium problem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:254:y:2015:i:c:p:39-48

DOI: 10.1016/j.amc.2014.12.135

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