Generalized mixed equilibrium problem in Banach spaces
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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.
Key wordssmall generalized mixed equilibrium problem variational inequality quasi-ϕ-nonexpansive mapping maximal monotone operator monotone mapping
Chinese Library ClassificationO177.5
2000 Mathematics Subject Classification47J05 47H09 49J25
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