Fiberwise contraction mappings principle
type: Item
instance of: scholarly article
title: Fiberwise contraction mappings principle
zbMATH Open document ID: 1305.54055
published in: Topology and its Applications
publication date: 2014-10-24T00:00:00Z
review text: A metric on a mapping \(f\) of a nonempty set \(X\) to a topological space \(Z\) is a pseudometric \(p\) on \(X\) such that it is a metric on every fibre \(f^{-1}z\) of \(f, z \in Z\). A metric mapping \((f, p)\) consisting of a mapping \(f\) of a set to a space and of a metric mapping \((f, p)\) is called a fibrewise complete if \(p\) is a complete metric on every \(f\). For details refer to \textit{B. A. Pasynkov} [Mosc. Univ. Math. Bull. 54, No. 3, 29--32 (1999); translation from Vestn. Mosk. Univ., Ser. I 1999, No. 3, 29--32 (1999; Zbl 0949.54038)]. The main purpose of this paper is to extend the well-known classical Banach contraction theorem to metric mappings.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 6361150
zbMATH Keywords: fixed point
zbMATH Keywords: Banach contraction
zbMATH Keywords: metric mapping
zbMATH Keywords: fibrewise completeness
author: B. A. Pasynkov
MaRDI profile type: Publication
full work available at URL: j.topol.2014.08.026
OpenAlex ID: W2013676194
cites work: On metric mappings
cites work: Q3814390
DOI: 10.1016/J.TOPOL.2014.08.026
description: scientific article; zbMATH DE number 6361150