Convergence analysis of iterative sequences for a pair of mappings in Banach spaces

Let C be a nonempty closed convex subset of a real Banach space E. Let S: C . C be a quasi-nonexpansive mapping, let T: C . C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F:= {x . C: Sx = x and Tx = x} . 0. Let {x n } n.0 be the sequence generated from an arbitrary x 0 . C by xn+1=(1.cn)Sxn+cnTnxn,n.0. We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {x n } to an element of F. These extend and improve the recent results of Moore and Nnoli