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Generalized mixed equilibrium problem in Banach spaces

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Abstract

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-ϕ-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

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Authors and Affiliations

  1. Department of Mathematics, Yibin University, Yibin, 644007, Sichuan Province, P. R. China

    Shi-sheng Zhang  (张石生)

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  1. Shi-sheng Zhang  (张石生)
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Correspondence to Shi-sheng Zhang  (张石生).

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Contributed by Shi-sheng ZHANG

Project supported by the Natural Science Foundation of Yibin University (No. 2009Z003)

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Zhang, Ss. Generalized mixed equilibrium problem in Banach spaces. Appl. Math. Mech.-Engl. Ed. 30, 1105–1112 (2009). https://doi.org/10.1007/s10483-009-0904-6

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  • DOI: https://doi.org/10.1007/s10483-009-0904-6

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