Approximation of convex functions
type: Item
instance of: scholarly article
title: Approximation of convex functions
zbMATH Open document ID: 1075.26003
author: J. J. Koliha
published in: Real Analysis Exchange
publication date: 2005-03-07T00:00:00Z
review text: It is known [\textit{M. Ghomi}, Proc. Am. Math. Soc. 130, No.~8, 2255--2259 (2002; Zbl 0999.26008)] that every convex function on an open interval \(I\) can be uniformly approximated by convex \(C^\infty\)-functions on every compact subinterval \([a,b]\) of \(I\). Ghomi's approach requires the knowledge of Lebesgue integral and convolutions. The aim of the paper under review is to give an elementary proof of the above mentioned approximation property requiring only first year calculus and linear algebra.
reviewed by: Wiesław Pleśniak
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 26E10
zbMATH DE Number: 2141364
zbMATH Keywords: convex function
zbMATH Keywords: convex \(C^\infty\)-function
zbMATH Keywords: approximation
MaRDI profile type: Publication
full work available at URL: realanalexch.29.1.0465
OpenAlex ID: W1573365996
DOI: 10.14321/REALANALEXCH.29.1.0465
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description: scientific article; zbMATH DE number 2141364