A comparison of various noncommuting conditions in metric fixed point theory and their applications
type: Item
instance of: scholarly article
title: A comparison of various noncommuting conditions in metric fixed point theory and their applications
zbMATH Open document ID: 1341.54023
DOI: 10.1186/1687-1812-2014-38
author: Ravi P. Agarwal
author: Nazeer Shahzad
author: Ravindra K. Bisht
published in: Fixed Point Theory and Applications
publication date: 2015-03-20T00:00:00Z
review text: It is well known that transforming a fixed point result for a single-valued mapping \(f:X\to X\) under some contractive-type condition into a common fixed point for two mappings \(f,g:X\to X\) usually requires some commutativity-type condition for these mappings. The article under review is a very good survey of various conditions of this kind that have appeared in the literature during more than three decades. Namely, the authors list and discuss more than 40 conditions, starting from the notion of weakly commuting mappings of \textit{S. Sessa} [Publ. Inst. Math., Nouv. Sér. 32(46), 149--153 (1982; Zbl 0523.54030)]. In most cases, examples are provided showing the difference between introduced concepts. Also, the (non)-usefulness of these concepts in coincidence and common fixed point results is discussed. The (far from complete) list of 144 references shows that the related problems attracted a lot of researchers. Finally, some of many possible applications of coincidence and common fixed point results (here, to differential equations and approximation theory) are presented as illustrations.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54-02
zbMATH DE Number: 6417858
zbMATH Keywords: common fixed point
zbMATH Keywords: \(R\)-weakly commuting mappings, compatible mappings
zbMATH Keywords: weakly compatible mappings
zbMATH Keywords: starshaped set
zbMATH Keywords: best approximation
zbMATH Keywords: best simultaneous approximation
zbMATH Keywords: convex metric space
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: \(R\)-subcommuting
zbMATH Keywords: \(R\)-subweakly commuting mappings
Wikidata QID: Q59401430
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1186/1687-1812-2014-38
OpenAlex ID: W2161600389
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