Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems. (English) Zbl 1234.49008
Summary: In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.
MSC:
| 49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
| 47H10 | Fixed-point theorems |
| 49M05 | Numerical methods based on necessary conditions |
Keywords:
variational inclusion; mixed equilibrium problem; fixed point; optimization problem; nonexpansive mapping; strong convergenceReferences:
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