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Zbl 1178.47051
Zhang, Shi-sheng
Generalized mixed equilibrium problem in Banach spaces. (English)
[J] Appl. Math. Mech., Engl. Ed. 30, No. 9, 1105-1112 (2009). ISSN 0253-4827; ISSN 1573-2754/e

From the summary: 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-$\varphi$-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study an optimization problem.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H05 Monotone operators (with respect to duality)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J20 Inequalities involving nonlinear operators

Keywords: hybrid algorithm; small generalised mixed equilibrium problem; common fixed points; variational inequalities; quasi-$\varphi$-nonexpansive mappings; maximal monotone operator; monotone mappings

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Zentralblatt MATH Berlin [Germany]