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In this paper by using $W_{n}$-mapping, we introduce a composite iterativemethod for finding a common fixed point for infinite family of nonexpansivemappings and a solution of a certain variational inequality. Furthermore, thestrong convergence of the proposed iterative method is established. Finally,some simulation examples are presented. Our results improve and extend theprevious results.

Convergence of general composite iterative method for infinite family of nonexpansive mappings in Hilbert spaces