A fixed point theorem for weakly inward multivalued contractions
type: Item
instance of: scholarly article
title: A fixed point theorem for weakly inward multivalued contractions
zbMATH Open document ID: 0957.47040
author: Teck-Cheong Lim
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-03-09T00:00:00Z
review text: Using transfinite induction the author proves the following fixed point theorem: Let \(D\) be a nonempty closed subset of a Banach space \(X\) and let \(T\) be a mapping assigning to \(x\in D\) a nonempty closed set \(T(x)\subset X\). Assume that \(T\) is contractive with respect to the Hausdorff metric and that \(Tx\) is contained in the closure of \(x+\{\lambda(z-x)\mid z\in D\), \(\lambda\geq 1\}\) for each \(x\in D\). Then there is an \(x\in D\) such that \(x\in Tx\).
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1497307
zbMATH Keywords: fixed point theorems
zbMATH Keywords: multivalued contraction
zbMATH Keywords: weakly inward mapping
zbMATH Keywords: transfinite induction
reviewed by: Christian Fenske
MaRDI profile type: Publication
OpenAlex ID: W2145095698
cites work: Q4000472
cites work: Q4150254
cites work: A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space
cites work: Differential Equations on Closed Subsets of a Banach Space
cites work: A remark on weakly inward contractions
cites work: Multivalued nonexpansive mappings in Banach spaces
cites work: Fixed point theorems for weakly inward multivalued mappings and their randomizations
DOI: 10.1006/JMAA.2000.6866
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description: scientific article; zbMATH DE number 1497307