Contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances
type: Item
instance of: scholarly article
title: Contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances
zbMATH Open document ID: 1233.54019
author: Kazimierz Włodarczyk
author: Robert Plebaniak
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-01-04T00:00:00Z
review text: \textit{S. Leader} [``Equivalent Cauchy sequences and contractive fixed points in metric spaces'', Stud. Math. 76, 63--67 (1983; Zbl 0469.54028)] proved two fixed point theorems for contractive mappings \(T\), with a complete graph, on a metric space. In the present paper, the authors consider the following question: If the spaces \(X\) are uniform with \(\mathcal T\)-families of generalized pseudo-distances, under what conditions does the fixed point theorem of Leader type for self-maps \(T\) on \(X\) hold even in the case where the spaces are not sequentially complete and the maps \(T\) do not have complete graphs? Answering this question affirmatively, the authors define the \(\mathcal T\)-family of generalized pseudo-distances, apply it to construct \(\mathcal T\)-contractions of Leader type on \(X\), and provide conditions guaranteeing the existence and uniqueness of fixed points of these contractions and the convergence to these fixed points of all iterative sequences of these contractions. Examples are constructed to illustrate the results obtained.
reviewed by: Srinivasa Swaminathan
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 5994318
zbMATH Keywords: fixed point
zbMATH Keywords: contraction of Leader type
zbMATH Keywords: uniform space
zbMATH Keywords: locally convex space
zbMATH Keywords: metric space
zbMATH Keywords: generalized pseudodistance
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.09.006
OpenAlex ID: W1973327465
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DOI: 10.1016/J.JMAA.2011.09.006
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description: scientific article; zbMATH DE number 5994318