Set-contractions and ball-contractions in some classes of spaces
type: Item
instance of: scholarly article
title: Set-contractions and ball-contractions in some classes of spaces
zbMATH Open document ID: 0679.47028
DOI: 10.1016/0022-247X(88)90121-7
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let X be a Banach space, D an arbitrary subset of X, and T: \(D\to X\) a set condensing mapping. The main result of this paper states that: If \(X=\ell^ p\), \(1\leq p\leq +\infty\), then T is ball-condensing. It is also shown that the above result does not hold for \(X=L^ p[0,1]\), \(1\leq p<+\infty\), \(p\neq 2\).
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 4113349
zbMATH Keywords: set-contractions
zbMATH Keywords: ball-contractions
zbMATH Keywords: set condensing mapping
zbMATH Keywords: ball- condensing
author: Tomás Domínguez Benavides
reviewed by: S. N. Mishra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4113349