Some results on existence and approximation in metric fixed point theory
type: Item
instance of: scholarly article
title: Some results on existence and approximation in metric fixed point theory
zbMATH Open document ID: 0936.54041
DOI: 10.1016/S0377-0427(99)00249-6
author: L. Saliga
author: W. A. Kirk
published in: Journal of Computational and Applied Mathematics
publication date: 2000-05-21T00:00:00Z
review text: Let \((M, d)\) be a metric space and let \(T: M\to M\) be a selfoperator. If we denote \(F(x)= d(x,Tx)\), \(x\in M\), we obtain a real function, whose so-called regular-global-inf property may be successfully used in order to obtain fixed point results, without assuming any continuity condition on the involved operator \(T\). The authors obtain in the paper under review such kind of results in both metric and Banach space setting, by considering various classes of (generalized) contractions.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1398420
zbMATH Keywords: weak regular-global-inf function
zbMATH Keywords: global minimum point
zbMATH Keywords: complete metric space
zbMATH Keywords: fixed point set
zbMATH Keywords: Picard iterates
zbMATH Keywords: Kuratowski measure of noncompactness
reviewed by: Vasile Berinde
MaRDI profile type: Publication
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Wikidata QID: Q127647367
description: scientific article; zbMATH DE number 1398420