Iterative sequence for asymptotically demicontractive maps in Banach spaces

Let E be a real Banach space and T :E→E an asymptotically demicontractive and uniformly LLipschitzian map with F(T ) := {x ∈ E: T x = x} =∅. We prove necessary and sufficient conditions for the strong convergence of the Mann iterative sequence to a fixed point of T .  2004 Published by Elsevier Inc.