Weak contractions, common fixed points, and invariant approximations
type: Item
instance of: scholarly article
title: Weak contractions, common fixed points, and invariant approximations
zbMATH Open document ID: 1183.47049
DOI: 10.1155/2009/390634
author: Nawab Hussain
author: Yeol Je Cho
published in: Journal of Inequalities and Applications
publication date: 2009-11-03T00:00:00Z
full work available at URL: https://eudml.org/doc/117797
review text: The concept of weak contraction was extended to the notion of \((\theta, L)\)-weak contraction by \textit{V.\,Berinde} [``On the approximation of fixed points of weak contractive mappings'', Carpathian J.~Math.\ 19, No.\,1, 7--22 (2003; Zbl 1114.47045)]. In this paper, the authors extend the concept of \((\theta, L)\)-weak contraction and introduce the notion of \((f,\theta, L)\)-weak contraction. For the underlying concept, the authors first establish a common fixed point result and then apply it to get a result in the field of approximation.
reviewed by: Hemant Kumar Nashine
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 5624544
zbMATH Keywords: weak contraction
zbMATH Keywords: \((\theta, L)\)-weak contraction
zbMATH Keywords: fixed point
zbMATH Keywords: best approximation
zbMATH Keywords: Opial's condition
Wikidata QID: Q59248934
MaRDI profile type: Publication
OpenAlex ID: W2137227374
cites work: An Introduction to Metric Spaces and Fixed Point Theory
cites work: Q4663557
cites work: Q3526313
cites work: Q4365248
cites work: A Generalization of Banach's Contraction Principle
cites work: Contractive type non-self mappings on metric spaces of hyperbolic type
description: scientific article; zbMATH DE number 5624544