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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 $\alpha $-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.

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
Full Text: DOI
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