Convergence Analysis of Iterative Sequences for a Pair of Mappings in Banach Spaces

Abstract. 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} 6 = ∅. Let {xn}n≥0 be the sequence generated from an arbitrary x0 ∈ C by xn+1 = (1 − cn)Sxn + cnT nxn, n ≥ 0. We prove necessary and sufficient conditions for the strong convergence of the iterative se-quence {xn} to an element of F. These extend and improve recent results of Moore and Nnoli