A fixed point theorem for multivalued mappings with \(\delta\)-distance
type: Item
instance of: scholarly article
title: A fixed point theorem for multivalued mappings with \(\delta\)-distance
zbMATH Open document ID: 1469.54033
DOI: 10.1155/2014/497092
author: Özlem Acar
author: Ishak Altun
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We mainly study fixed point theorem for multivalued mappings with \(\delta\)-distance using Wardowski's technique on complete metric space. Let \((X, d)\) be a metric space and let \(B(X)\) be a family of all nonempty bounded subsets of \(X\). Define \(\delta : B(X) \times B(X) \rightarrow \mathbb{R}\) by \(\delta(A, B) = \text{sup} \left\{d(a, b) : a \in A, b \in B\right\} \). Considering \(\delta\)-distance, it is proved that if \((X, d)\) is a complete metric space and \(T : X \rightarrow B(X)\) is a multivalued certain contraction, then \(T\) has a fixed point.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 7022493
Wikidata QID: Q59038803
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/497092
OpenAlex ID: W2001838579
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description: scientific article; zbMATH DE number 7022493