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In this paper, we introduce an iterative method for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusions with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of an equilibrium problem in Hilbert spaces. Furthermore, using our new iterative scheme, under suitable conditions, we prove some strong convergence theorems for approximating these common elements. The results presented in the paper improve and extend many recent important results. © 2013 Deng and Chen; licensee Springer.

journal of inequalities and applications

A hybrid approximation algorithm for finding common solutions of equilibrium problems, a finite family of variational inclusions, and fixed point problems in Hilbert spaces