A general iterative method for nonexpansive mappings in Hilbert spaces

Let H be a real Hilbert space. Consider on H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0 < ce < 1, and a strongly positive linear bounded operator A with coefficient (gamma) over bar > 0. Let 0 < gamma < (gamma/alpha) over bar. It is proved that the sequence {x(n)} generated by the iterative method x(n+1) = (I - alpha(n)A)Tx(n)+ alpha(n)gamma f (x(n)) converges strongly to a fixed point (x) over bar is an element of Fix(T) which solves the variational inequality ((gamma f - A)(x) over tilde, x-(x) over bar <= 0 for x is an element of Fix(T). (c) 2005 Elsevier Inc. All rights reserved.