General iterative algorithms for mixed equilibrium problems, variational inequalities and fixed point problems. (English) Zbl 1322.49018
Summary: In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a mixed equilibrium problem, a general system of variational inequalities and a fixed-point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problems. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature.
MSC:
| 49J40 | Variational inequalities |
| 47J25 | Iterative procedures involving nonlinear operators |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H05 | Monotone operators and generalizations |
| 47H10 | Fixed-point theorems |
| 65K15 | Numerical methods for variational inequalities and related problems |
Keywords:
mixed equilibrium problems; variational inequalities; fixed-points; iterative algorithm; nonexpansive mappings; strongly positive operator; inverse strongly monotone mappingReferences:
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