Convergence Analysis of Iterative Sequences for a Pair of Mappings in Banach Spaces
نویسندگان
چکیده
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 xn, n ≥ 0. We prove necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F . These extend and improve recent results of Moore and Nnoli.
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