Abstract
Let H be a Hilbert space and let and
be the countable families of nonexpansive mappings of H into itself such that
. Assume that F is a nonlinear operator which is κ-Lipschitzian and η-strong monotone on C. In this article, we devise a new iterative scheme {x
n
} from an arbitrary initial point x
0∈H for the countable family of nonexpansive mappings
and
and prove that {x
n
} strongly converges to the unique solution x* of the variational inequality