Fixed point theorems for Lipschitzian type mappings in \(CAT(0)\) spaces
type: Item
instance of: scholarly article
title: Fixed point theorems for Lipschitzian type mappings in \(CAT(0)\) spaces
zbMATH Open document ID: 1262.47077
author: M. Abbas
author: Zoran Kadelburg
author: D. R. Sahu
published in: Mathematical and Computer Modelling
publication date: 2013-01-27T00:00:00Z
review text: The purpose of the paper is to investigate the demiclosedness principle, the existence and iterative approximation for fixed points for nearly asymptotically nonexpansive mappings in the framework of \(CAT(0)\) spaces. The authors prove \(\Delta\)-convergence and strong convergence of the Ishikawa scheme: \[ \begin{aligned} x_{n+1}&=(1-\alpha_n)x_n\bigoplus \alpha_nT^ny_n,\\ y_{n}&=(1-\beta_n)x_n\bigoplus \beta_nT^nx_n, \;n\in \mathbb{N}, \end{aligned} \] where \(\mathbb{N}\) stands for the set of natural numbers, \(\{\alpha_n\}\) and \(\{\beta_n\}\) are real sequences in \((0,1)\), and \(T\) is a nearly asymptotically nonexpansive self-mapping defined on a convex subset of a \(CAT(0)\) space. The present results generalize, extend and unify some recent results in the literature.
reviewed by: M. F. Bota-Boriceanu
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 6131048
zbMATH Keywords: iteration process
zbMATH Keywords: nearly asymptotically quasi-nonexpansive mappings
zbMATH Keywords: fixed point
zbMATH Keywords: CAT(0) space
MaRDI profile type: Publication
full work available at URL: j.mcm.2011.10.019
OpenAlex ID: W1991082563
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DOI: 10.1016/J.MCM.2011.10.019
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description: scientific article; zbMATH DE number 6131048