## A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.(English)Zbl 1186.47075

Summary: We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of a variational inclusion with set-valued maximal monotone mapping, and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating these common elements are proved. The results presented in the paper improve and extend the main results of J. W. Peng, Y. Wang, D. S. Shyu and J.-C. Yao [J. Inequal. Appl. 2008, Article ID 720371 (2008; Zbl 1161.65050)] and many others.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H05 Monotone operators and generalizations 47J22 Variational and other types of inclusions

Zbl 1161.65050
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### References:

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