Abstract
In this paper, we prove strong convergence for the modified Ishikawa iteration process of a total asymptotically nonexpansive mapping satisfying condition (A) in a real uniformly convex Banach space. Our result generalizes the results due to Rhoades (J. Math. Anal. Appl. 183:118-120, 1994).MSC:47H05, 47H10.
Highlights
1 Introduction Let X be a real Banach space, let C be a nonempty closed convex subset of X, and let T be a mapping of C into itself
Let X be a real uniformly convex Banach space, let C be a nonempty closed convex subset of X, and let T be a nonexpansive mapping of C into itself satisfying condition (A) with F(T) = ∅
We prove that if T is a total asymptotically nonexpansive self-mapping satisfying condition (A), the iteration {xn} defined by ( . ) converges strongly to some fixed point of T, which generalizes the results due to Rhoades [ ]
Summary
1 Introduction Let X be a real Banach space, let C be a nonempty closed convex subset of X, and let T be a mapping of C into itself. T is said to be asymptotically nonexpansive [ ] if there exists a sequence {kn}, kn ≥ , with limn→∞ kn = , such that
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