On nearly uniformly convex sets
type: Item
instance of: scholarly article
title: On nearly uniformly convex sets
zbMATH Open document ID: 0756.52004
DOI: 10.1007/BF01198964
author: D. Kutzarova
author: Stefan Rolewicz
published in: Archiv der Mathematik
publication date: 1992-09-27T00:00:00Z
review text: Let \(C\) be a closed convex set in a real Banach space \(X\). \(C\) is called nearly uniformly convex with respect to a center \(a\in C\) if for every \(\varepsilon>0\) there is a \(\delta\), \(0<\delta<1\), such that for every set \(E\subset C\) with \(\alpha(E)>\delta\), one has \(E\cap(a+(1-\delta)(C- a))\neq\emptyset\), where \(\alpha(E)\) means the index of noncompactness by K. Kuratowski. In the present paper several properties of nearly uniformly convex sets in Banach spaces are investigated.
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 62243
zbMATH Keywords: nearly uniformly convex sets
zbMATH Keywords: Banach spaces
reviewed by: Valeriu Soltan
MaRDI profile type: Publication
cites work: Q3746314
cites work: Banach spaces which are nearly uniformly convex
cites work: On drop property for convex sets
cites work: Drop property equals reflexivity
cites work: A uniform geometric property of Banach spaces
cites work: Q3784621
cites work: On ∆-uniform convexity and drop property
full work available at URL: https://doi.org/10.1007/bf01198964
OpenAlex ID: W2056105263
description: scientific article; zbMATH DE number 62243