The variational principle and fixed point theorems in certain topological spaces
type: Item
instance of: scholarly article
title: The variational principle and fixed point theorems in certain topological spaces
zbMATH Open document ID: 0859.54042
author: Jin-Xuan Fang
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-04-07T00:00:00Z
review text: The author introduces the concept of \(F\)-type topological space and gives a characterization of this kind of spaces. He points out that the usual metric spaces, Hausdorff topological vector space and Menger space are all special cases of \(F\)-type space. Using this concept, some fixed point theorems and a variational principle in \(F\)-type topological space are established. As an application, the author utilizes the results presented in this paper to obtain a variational principle and a fixed point theorem in Menger probabilistic metric spaces, which generalize the corresponding results of \textit{I. Ekeland} [ibid. 47, 324-353 (1974; Zbl 0286.49015)], \textit{J. Caristi} [Trans. Am. Math. Soc. 215, 241-251 (1976; Zbl 0305.47029)] and the reviewer with \textit{Chen Yuqing} and \textit{Guo Jinli} [Acta Math. Appl. Sin., Engl. Ser. 7, No. 3, 217-228 (1991; Zbl 0743.54017)].
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 930198
zbMATH Keywords: Ekeland's variational principle
zbMATH Keywords: Caristi's fixed point theorem
zbMATH Keywords: \(F\)-type topological space
reviewed by: Shihsen Chang
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0323
OpenAlex ID: W2006323766
DOI: 10.1006/JMAA.1996.0323
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description: scientific article; zbMATH DE number 930198