Abstract
In this paper we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings on CAT(0) spaces. We prove a strong convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm.
Highlights
Let ( X, d) be a given metric space and let x, y be two poins in X with d( x, y) = l
We call ( X, d) a geodesic space if every two points of X can be joined by a geodesic segment
In this paper, inspired by the Algorithms (1) and (2), we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings in CAT(0) spaces
Summary
A mapping T is called asymptotically nonexpansive [12] if there exists a sequence {k n } ⊂ [1, ∞) such that k n → 1 as n → ∞ and, for every n ∈ N : d( T n x, T n y) ≤ k n d( x, y), ∀ x, y ∈ C. A mapping T is called totally asymptotically quasi-nonexpansive if Fix ( T ) 6= ∅ and there exist null sequences {un }∞. In 2016, Huang in [21], introduced the following algorithm for a family of nonexpansive mappings in a CAT(0) space: L xn+1 = αn f ( xn ) (1 − αn ) Tn ( xn ), n ≥ 1 where {αn }∞. In this paper, inspired by the Algorithms (1) and (2), we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings in CAT(0) spaces. We provide two numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm
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