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A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping. (English) Zbl 1163.49003
Summary: The purpose of this paper is to present an iterative scheme by a hybrid method for finding a 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 α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space.

MSC:
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H05Monotone operators (with respect to duality) and generalizations
49M30Other numerical methods in calculus of variations
47J20Inequalities involving nonlinear operators