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

Plubtieng, Somyot; Punpaeng, Rattanaporn

Appl. Math. Comput. 197, No. 2, 548-558 (2008).

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)].

Reviewer: B. Döring (Düsseldorf)

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.

Keywords:

nonexpansive mapping; equilibrium problem; fixed point; \(\alpha\)-inverse-strongly monotone mapping; variational inequality; strictly pseudocontractive mapping

Citations:

Zbl 1121.65064

References:

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