Strong Convergence Theorem For Iterative Sequences In Banach Spaces

Let E be a real Banach space with a uniformly Gateaux differentiable norm, D be a nonempty closed convex E and f be a contractive mapping, T:Dâ†'D be an asymptotically nonexpansive mapping. Define{xn} in the following way: and It is show that under some suitable conditions, the sequences{xn} converge strongly to some of fixed points of T.Let E be a uniformly smooth Banach space, D be a nonempty closed convex E and f be a contractive mapping, T:Dâ†'D be an nonexpansive mapping. Let{xn} be a composite iteration process defined by It is show that under some suitable conditions, the sequence{xn} converges strongly to a fixed point of T.The results presented in this paper extend and improve results of Zhao Liangcai and many others.