Approximation theorems for solving common solution of a system of mixed equilibrium problems and variational inequality problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense. (English) Zbl 1285.47083
Summary: In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly Lipschitzian continuous and asymptotically \(\lambda_{i}\)-strict pseudocontractive mapping in the intermediate sense. We prove the strong convergence for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give some numerical examples to support our results.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
Keywords:
asymptotically strict pseudocontraction in the intermediate sense; hybrid projection method; system of mixed equilibrium problem; fixed pointsReferences:
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