Let Cbe a non-empty closed convex subset of real Banach space E. Let  be non-expansive mapping and let  be a uniformly L-Lipschitizian, asymptotically demicontractive mapping with sequence    such that    and    Assume that  Let  and  be a sequence in  satisfying (i)  (ii)    For arbitrary  let  be a sequence iteratively defined by      Then we prove that the sequence  converges strongly at the common fixed point pof Sand T.

nonexpansive, uniformly L-Lipschitzian, asymptotically demicontractive, hybrid implicit S-iterative scheme, strong convergence.