Abstract
AbstractAn existence theorem for a fixed point of anα-nonexpansive mapping of a nonempty bounded, closed and convex subset of a uniformly convex Banach space has been recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishikawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also extended toCAT(0)spaces.AMS Subject Classification:54E40, 54H25, 47H10, 37C25.
Highlights
1 Introduction The purpose of this paper is to study fixed point theorems of α-nonexpansive mappings of CAT( ) spaces
An existence theorem for a fixed point of an α-nonexpansive mapping T of a nonempty bounded, closed and convex subset C of a uniformly convex Banach space E has been recently established by Aoyama and Kohsaka [ ] with a non-constructive argument
We introduce the notion of α-nonexpansive mappings of CAT( ) spaces
Summary
The purpose of this paper is to study fixed point theorems of α-nonexpansive mappings of CAT( ) spaces. 3 Fixed point and convergence theorems in Banach spaces Lemma . . If {xn} is bounded and lim infn→∞ Txn – xn = , the fixed point set F(T) = ∅.
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