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Generalized mixed equilibrium problem in Banach spaces. (English) Zbl 1178.47051
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-$\phi$-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study an optimization problem.
##### MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H09 Mappings defined by “shrinking” properties 47H05 Monotone operators (with respect to duality) and generalizations 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47J20 Inequalities involving nonlinear operators
##### References:
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