An unbounded closed nearly uniformly convex set
type: Item
instance of: scholarly article
title: An unbounded closed nearly uniformly convex set
zbMATH Open document ID: 0745.46022
DOI: 10.1007/BF01194242
author: Pei-Kee Lin
published in: Archiv der Mathematik
publication date: 1993-01-01T00:00:00Z
review text: Let \(C\) be a nonempty proper closed convex subset of a real Banach space \(X\). \(C\) is daid to be nearly uniformly convex (NUC) (respectively, NUC\('\))) with a center \(a\in C\) if for every \(\varepsilon>0\), there exists a \(\delta\), \(1>\delta>0\), such that for every \(\varepsilon\)- separate sequence in \(C\), \[ \text{co}(x_ n)\cap(a+(1-\delta)(C- a))\neq\emptyset\qquad\hbox{(respectively, } \overline{co}(x_ n)\cap(a+(1-\delta)(C-a))\neq\emptyset\text{).} \] The author showed there is an unbounded nearly uniformly convex set in Hilbert space. This gives an answer of a question of Kutzarova and Rolewicz.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 4216543
zbMATH Keywords: unbounded nearly uniformly convex set in Hilbert space
reviewed by: Ke-Pao Lin
MaRDI profile type: Publication
cites work: On nearly uniformly convex sets
cites work: Q4136031
full work available at URL: https://doi.org/10.1007/bf01194242
OpenAlex ID: W2010989456
description: scientific article; zbMATH DE number 4216543