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A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings. (English) Zbl 1154.47053

Authors’ abstract: We introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for \(\alpha\)-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main theorem extends a recent result of Y.–H.Yao and J.–C.Yao [Appl.Math.Comput.186, No.2, 1551–1558 (2007; Zbl 1121.65064)].

MSC:

47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Citations:

Zbl 1121.65064
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References:

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