Fixed point theorems of local contraction mappings on Menger spaces
type: Item
instance of: scholarly article
title: Fixed point theorems of local contraction mappings on Menger spaces
zbMATH Open document ID: 0758.54015
DOI: 10.1007/BF02020399
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1992-09-27T00:00:00Z
review text: The concept of \(\varepsilon\)-chainable PM-space is introduced, which is a strengthening form of the well-known definition of \((\varepsilon,\lambda)\)-chainable PM-space. By using this concept and under some additional conditions, the author proves some fixed point theorems for single-valued and set-valued local contraction mappings on this kind of spaces. The results presented in this paper extend the corresponding results for local contraction mappings on metric spaces given in [\textit{M. Edelstein}, Proc. Am. Math. Soc. 12, 7-10 (1961; Zbl 0096.171) and \textit{P. K. F. Kuhfittig}, Pac. J. Math. 65, No. 2, 399-403 (1976; Zbl 0335.54035)].
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E70
zbMATH DE Number: 61754
zbMATH Keywords: local contraction mapping
zbMATH Keywords: \(\varepsilon\)-chainable PM-space
author: Jin-Xuan Fang
reviewed by: Shihsen Chang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 61754