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An Iterative Method for Mixed Point Problems of Nonexpansive and Monotone Mappings and Generalized Equilibrium Problems

Commun. Math. Anal.
Volume 12, Number 1 (2012), 76 - 95

An Iterative Method for Mixed Point Problems of Nonexpansive and Monotone Mappings and Generalized Equilibrium Problems

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Abstract

In this paper, we introduce an iterative scheme for finding the common element of the set of fixed points of a countable family of nonexpansive mappings, the set of solutions of variational inequality for μ-Lipschitzian, relaxed (λ,γ)-cocoercive mapping and the set of solutions of a generalized equilibrium problem. We show that the iterative sequence converges strongly to a common element of the three sets. Our results generalize many recent results, for example, the results of B. Ali [2].