Generalized Caristi's fixed point theorems
type: Item
instance of: scholarly article
title: Generalized Caristi's fixed point theorems
zbMATH Open document ID: 1171.54031
DOI: 10.1155/2009/170140
author: A. Latif
published in: Fixed Point Theory and Applications
publication date: 2009-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/55933
review text: Using the concept of \(w\)-distance [\textit{O. Kada, T. Suzuki} and \textit{W. Takahashi}, Math. Jap. 44, No.~2, 381--391 (1996; Zbl 0897.54029)], the following generalization of Caristi's fixed point theorem is proved: Let \(X\) be a complete metric space, \(\psi: X \rightarrow [0, \infty)\) be a lower semicontinuous function and \(w\) be a \(w\)-distance on \(X\). Let \(g:X\rightarrow (0, \infty)\) be a function such that for some \(r>0\), \[ \sup\{g(x):x\in X, \psi(x)\leq\inf_{z\in X}\psi(z)+r\}<\infty. \] Let \(T: X\rightarrow 2^X\) be a multivalued map such that for each \(x\in X\) there exists \(y\in T(x)\) satisfying \[ w(x,y)\leq g(x)(\psi(x)-\psi(y)). \] Then \(T\) has a fixed point \(x_0\in X\) such that \(w(x_0, x_0)=0.\)
reviewed by: Dorel Miheţ
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 5574352
zbMATH Keywords: Caristi fixed point theorem
zbMATH Keywords: \(w\)-distance
zbMATH Keywords: multivalued maps
Wikidata QID: Q59248951
MaRDI profile type: Publication
OpenAlex ID: W2081175251
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description: scientific article; zbMATH DE number 5574352