In this paper, we introduce a new general iterative process for approximating
a common fixed point of a semigroup of nonexpansive mappings, with respect
to strongly left regular sequence of means defined on an appropriate space of
bounded real-valued functions of the semigroups and the set of solutions a system
of variational inequality for finite family of inverse strongly monotone mappings
in a real Hilbert space. Our result extends and improves the result announced
by H. Piri and A.H. Badali [13] and some others.