Abstract
A one-step iteration with errors is considered for a family of asymptotically nonexpansive nonself mappings. Weak convergence of the purposed iteration is obtained in a Banach space.
Highlights
Introduction and PreliminariesLet E be a real Banach space and E∗ the dual space of E
Let C be a nonempty closed and convex subset of E and T a mapping
Let E be a real uniformly convex Banach space, K a nonempty closed, and convex subset of E and T : K → K an asymptotically nonexpansive mapping
Summary
Introduction and PreliminariesLet E be a real Banach space and E∗ the dual space of E. Let C be a closed convex subset of a uniformly convex Banach space E with a Frechet differential norm, T : C → C a nonexpansive mapping with a fixed point, and {αn} a real sequence such that 0 ≤ αn ≤ 1 and n 1 αn 1 − αn ∞.
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