Abstract
Let K be a nonempty closed and convex subset of a real Banach space E. Let T : K -> E be a continuous pseudocontractive mapping and f : K -> E be a continuous pseudocontractive mapping and f : K -> E a contraction, both satisfying weakly inward condition. Then for t is an element of (0, 1), there exists a sequence {y(t)} subset of K satisfying the following condition: y(t) = (1 - t)f (y(t)) + tT(y(t)). Suppose further that {y(t)} is bounded or F(T) not equal 0 and E is a reflexive Banach space having weakly continuous duality mapping J(phi) for some gaugy phi. Then it is proved that {y(t)} converges strongly to a fixed point of T, which is also a solution of certain variational inequality. Moreover, an explicit iteration process that converges strongly to a common fixed point of a finite family of nonexpansive mappings and hence to a solution of a certain variational inequality is constructed.