Minimization theorems for fixed point theorems in fuzzy metric spaces and applications
type: Item
instance of: scholarly article
title: Minimization theorems for fixed point theorems in fuzzy metric spaces and applications
zbMATH Open document ID: 0845.54004
DOI: 10.1016/0165-0114(94)90234-8
author: Jong Soo Jung
author: Yeol Je Cho
author: J. K. Kim
published in: Fuzzy Sets and Systems
publication date: 1996-09-23T00:00:00Z
review text: The authors prove a minimization theorem in fuzzy metric spaces. The theorem goes as follows: If \(X\) and \(Y\) are complete fuzzy metric spaces of a given type, \(f: X\to Y\) is closed and continuous and \(\varphi: f(X)\to (-\infty, \infty]\)\ is lower semicontinuous and bounded from below then under certain assumptions \(\varphi \circ f\) attains its minimum. Using the theorem above the authors obtain a variational principle as well as a fixed point theorem for fuzzy metric spaces. Finally the equivalence of these theorems is proved. The variational principle, the fixed point theorem and their equivalence also appear in \textit{M. Stojaković} and \textit{Z. Ovcin} [ibid. 66, 353-356 (1994; Zbl 0842.54020)].
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 788341
zbMATH Keywords: minimization theorem
zbMATH Keywords: variational principle
zbMATH Keywords: fixed point theorem
reviewed by: Osmo Kaleva
MaRDI profile type: Publication
full work available at URL: 0165-0114(94)90234-8
OpenAlex ID: W2038119776
cites work: Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
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cites work: The variational principle in fuzzy metric spaces and its applications
cites work: On fuzzy metric spaces
cites work: Statistical metric spaces
cites work: Q3976098
description: scientific article; zbMATH DE number 788341