Summary: Consider on a real Hilbert space a nonexpansive mapping with a fixed point, a contraction with coefficient , and two strongly positive linear bounded operators with coefficients and , respectively. Let . We introduce a general iterative algorithm defined by
with , and prove the strong convergence of the iterative algorithm to a fixed point which is the unique solution of the variational inequality (for short, . On the other hand, assume is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on . We devise another iterative algorithm which generates a sequence from an arbitrary initial point . The sequence is proven to converge strongly to an element of which is the unique solution of the . Applications to constrained generalized pseudoinverses are included.