Convergence results for fixed point iterations in \(\mathbb{R}\)
type: Item
instance of: scholarly article
title: Convergence results for fixed point iterations in \(\mathbb{R}\)
zbMATH Open document ID: 0848.65037
DOI: 10.1016/0898-1221(95)00188-3
publication date: 1996-07-08T00:00:00Z
review text: Let \(g:[a,b] \to \mathbb{R}\) satisfy the Lipschitz condition \(|g(x) - g(y)|< L |x - y|\), \(x,y \in [a,b]\). The authors consider the following iteration schemes for computing the fixed point of the mapping \(g\): \[ x_{n+1} = (1 - \lambda) x_n + \lambda g(x_n), \quad \lambda \in \mathbb{R} \tag{a} \] \[ x_{n + 1} = (1 - \alpha_n) x_n + \alpha_n g(x_n) \tag{b} \] for some real parameters \(\alpha_n\). New convergence conditions for (a) and (b) are derived.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 878517
zbMATH Keywords: fixed point iterations
zbMATH Keywords: convergence
author: Dragoslav Herceg
author: Nataša Krejić
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00188-3
OpenAlex ID: W2065066972
cites work: Fixed point theorems for set-valued mappings of contractive type
cites work: Krasnoselski's Theorem on the Real Line
cites work: Fixed Point Iterations Using Infinite Matrices
cites work: A Generalization of Krasnoselski's Theorem on the Real Line
cites work: Ishikawa's iterations of real Lipschitz functions
cites work: Comments on two fixed point iteration methods
cites work: Q3730500
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 878517