Iterative methods for mixed equilibrium problems and strictly pseudocontractive mappings. (English) Zbl 1475.47060
Summary: In this paper, we introduce new implicit and explicit iterative schemes for finding a common element of the set of solutions of the mixed equilibrium problem and the set of fixed points of a \(k\)-strictly pseudocontractive non-self mapping in Hilbert spaces. We establish results of the strong convergence of the sequences generated by the proposed schemes to a common point of two sets, which is a solution of a certain variational inequality. Our results extend and improve the corresponding results given by many authors recently in this area.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
mixed equilibrium problem; \(k\)-strictly pseudocontractive mapping; nonexpansive mapping; fixed points; \(\rho\)-Lipschitzian and \(\eta\)-strongly monotone operator; variational inequality; implicit iterative schemes; Hilbert space; strong convergenceReferences:
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