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-\(\varphi\)-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 involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H05 | Monotone operators and generalizations |
| 47H10 | Fixed-point theorems |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
Keywords:
hybrid algorithm; small generalised mixed equilibrium problem; common fixed points; variational inequalities; quasi-\(\varphi\)-nonexpansive mappings; maximal monotone operator; monotone mappingsReferences:
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