## 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.

Zbl 1121.65064
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### References:

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