  In this paper, first we introduce a new mapping for finding a common fixed
point of an infinite family of nonexpansive mappings then we consider iterative
method for finding a common element of the set of fixed points of an infinite
family of nonexpansive mappings, the set of solutions of an equilibrium problem
and the set of solutions of the variational inequality for
$\alpha$-inverse-strongly monotone mapping in a Hilbert space. We show that
under suitable conditions, the sequence converges strongly to a common element
of the above three sets. Our results presented in this paper improve and extend
other results.

Functional Analysis