Fixed point theory for contractive mappings satisfying \(\Phi \)-maps in G-metric spaces
type: Item
instance of: scholarly article
title: Fixed point theory for contractive mappings satisfying \(\Phi \)-maps in G-metric spaces
zbMATH Open document ID: 1204.54039
DOI: 10.1155/2010/181650
author: Yanyan Li
published in: Fixed Point Theory and Applications
publication date: 2010-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/232392
review text: The \(\varphi\)-contraction principle in a complete metric space is well known (see [\textit{J. Matkowski}, ''Integrable Solutions of Functional Equations,'' Dissertationes Math., Warszawa 127, 63 p. (1975; Zbl 0318.39005)]; \textit{I. A. Rus}, [Math., Rev. Anal. Numér. Théor. Approximation, Math. 24(47), 175--178 (1982; Zbl 0525.54029) and Generalized Contractions and Applications. Cluj-Napoca: Cluj University Press. (2001; Zbl 0968.54029)]; \textit{J. Jachymski} and \textit{M. Styborski}, Fixed point theory and its applications. Proceedings of the international conference, Bȩddlewo, Poland, August 1--5, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 77, 123-146 (2007; Zbl 1149.47044)]). In this paper a fixed point principle for \(\varphi\)-contractions in a complete G-metric space (see \textit{Z. Mustafa} and \textit{B. Sims}, [J. Nonlinear Convex Anal. 7, No. 2, 286--297 (2006; Zbl 1111.54025)]) is presented. Then a theory [\textit{I. A. Rus}, Fixed Point Theory 9, No. 2, 541--559 (2008; Zbl 1172.54030)] of this metrical fixed point theorem is discussed.
reviewed by: Ioan A. Rus
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 5792435
zbMATH Keywords: fixed point
zbMATH Keywords: G-metric space
zbMATH Keywords: \(\varphi\)-contraction
Wikidata QID: Q59253842
MaRDI profile type: Publication
OpenAlex ID: W2093510613
cites work: Q3410667
cites work: Some fixed point theorem for mapping on complete \(G\)-metric spaces
cites work: Q5465199
cites work: Fixed Point Theorems for Mappings with a Contractive Iterate at a Point
description: scientific article; zbMATH DE number 5792435