Quasiadditive properties and bilipschitz conditions
type: Item
instance of: scholarly article
title: Quasiadditive properties and bilipschitz conditions
zbMATH Open document ID: 0913.39019
published in: Aequationes Mathematicae
publication date: 1999-06-07T00:00:00Z
review text: Let \({\mathcal H}\) be the class of all positive nondecreasing functions \(f\) on \((0,+\infty)\), and let \[ S_f(x,y)= \bigl(f(x) +f(y) \bigr)/f(x+y). \] A function \(f\in {\mathcal H}\) is quasiadditive if \[ \lambda_f= \inf_{x,y>0} S_f(x,y)>0. \] A function \(f\in {\mathcal H}\) is quasimultiplicative if there exist positive constants \(a\) and \(b\) such that \[ a\leq {f(x)f(y) \over f(xy)}\leq b \] for all \(x,y\in (0,+\infty)\). In the paper the authors present a series of properties of quasiadditive and quasimultiplicative functions. Various Hölderian growth estimates are obtained and functional inequalities are proved for these functions.
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 1221001
zbMATH Keywords: quasiadditive mappings
zbMATH Keywords: quasimultiplicative functions
zbMATH Keywords: Hölderian growth estimates
zbMATH Keywords: functional inequalities
author: V. V. Aseev
author: M. K. Vamanamurthy
author: M. Vuorinen
reviewed by: Gian Luigi Forti
MaRDI profile type: Publication
full work available at URL: s000100050048
OpenAlex ID: W2091995154
DOI: 10.1007/S000100050048
description: scientific article; zbMATH DE number 1221001