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 L-Lipschitzian map with F(T):={x∈E:Tx=x}≠∅. We prove necessary and sufficient conditions for the strong convergence of the Mann iterative sequence to a fixed point of T.