Some theorems on function smoothing
type: Item
instance of: scholarly article
title: Some theorems on function smoothing
zbMATH Open document ID: 0891.46005
author: Igor G. Tsar'kov
published in: Moscow University Mathematics Bulletin
publication date: 1997-07-10T00:00:00Z
review text: Here is part of a sample theorem (Theorem 4): Let \(X\) be a real Banach space and \(B\) its unit ball. Then \(X\) is superreflexive if and only if, for each uniformly continuous real-valued function \(f\) on \(B\), \[ \inf|f-\varphi|_B= 0, \] where the infimum is taken over all \(\varphi: B\to\mathbb{R}\) which are Fréchet differentiable with uniformly continuous Fréchet derivative and \(|\cdot|_B\) denotes the sup-norm. The paper contains several other results which are too technical to be described here in more detail. Unfortunately, it is marred by typographical errors, some unexplained notation (even in the Russian original), and by the bad translation.
reviewed by: Klaus Dieter Bierstedt
Mathematics Subject Classification ID: 46B07
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46B10
zbMATH DE Number: 1028801
zbMATH Keywords: modulus of continuity
zbMATH Keywords: uniformly continuous function
zbMATH Keywords: Hölder continuous function
zbMATH Keywords: Fréchet differentiable function
zbMATH Keywords: modulus of convexity
zbMATH Keywords: uniformly convex space
zbMATH Keywords: superreflexive space
zbMATH Keywords: uniformly continuous Fréchet derivative
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1028801