Remark on the stability of the gamma functional equation
type: Item
instance of: scholarly article
title: Remark on the stability of the gamma functional equation
zbMATH Open document ID: 0929.39014
DOI: 10.1007/BF03322812
author: Horst Alzer
published in: Results in Mathematics
publication date: 2000-01-23T00:00:00Z
full work available at URL: https://eudml.org/doc/18331
review text: Let \(\delta>0\) and let \(f:(0,+\infty)\rightarrow (0,+\infty)\) satisfy \(| f(x+1)-xf(x)| \leq\delta\) for \(x>0\). It is proved that there exists a unique \(F:(0,+\infty)\rightarrow (0,+\infty)\) such that \(F(x+1)=xF(x)\) and (1) \(| f(x)-F(x)| \leq e\delta /x\) for \(x>0\), where \(e\) denotes Euler's number. Moreover, it is shown that \(e\) is the best possible constant in (1). This brief note generalizes a result obtained by \textit{S.-M. Jung} [Result. Math. 33, No. 3-4 , 306-309 (1998; Zbl 0907.39027)].
reviewed by: Janusz Morawiec
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1320612
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: gamma functional equation
MaRDI profile type: Publication
cites work: On the stability of gamma functional equation
OpenAlex ID: W2002528234
description: scientific article; zbMATH DE number 1320612