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 bea quasi-nonexpansive mapping,let T:C→C be an asymptotically demicontractive and uniformlyLipschitzian mapping,and let F:={x ∈ C:Sx=x and Tx=x}≠=φ.Let{X}be the sequencegenerated from an arbitrary x∈ C byx=(1-c)Sx+cT~nx,n≥0.We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence{x}to an element of F.These extend and improve the recent results of Moore and Nnoli.