Strong convergence theorems for uniformly continuous pseudocontractive maps

Let K be a nonempty closed convex subset of a real Banach space E and let T: K -> K be a uniformly continuous pseudocontraction. Fix any u epsilon K. Let {x(n)} be defined by the iterative process: X-0 epsilon K, x(n+1) := mu(n) (alpha(n)Tx(n) + (1 - alpha(n))alpha(n)) + (1 - mu(n))u. Let delta(epsilon) denote the modulus of continuity of T with pseudo-inverse phi. If {phi(t)/t: 0 < t < 1} and {xn} are bounded then, under some mild conditions on the sequences {alpha(n)}(n), and {mu(n)}(n), the strong convergence of {x(n)} to a fixed point of T is proved. In the special case where T is Lipschitz, it is shown that the boundedness assumptions on {phi(t)/t: 0 < t < I=1} and {x(n)} can be dispensed with. (c) 2005 Elsevier Inc. All rights reserved.