In this paper, we consider a variational inequality problem  where F, T are mappings from a real Hilbert space into itself and Fix T is the fixed points set of a demicontractive mapping T. We propose an iterative algorithm given as:

to find approximate solutions. Under some assumptions on F, T, w and  we establish the strong convergence of the sequence  generated by this schema to the solution of  An application to convex minimization is provided.

demicontractive mapping, quasi-nonexpansive mapping, fixed point, variational inequality, descent method.