On the graph of a quasi-additive function
type: Item
instance of: scholarly article
title: On the graph of a quasi-additive function
zbMATH Open document ID: 0706.39007
DOI: 10.1007/BF01833143
author: Elsie Sterbin Gottlieb
published in: Aequationes Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137344
review text: The author considers quasi-additive functions, i.e. functions \(f:X\to {\mathbb{R}}\) satisfying the condition \(| f(x+y)-f(x)-f(y)| \leq \epsilon \min \{| f(x+y)|,| f(x)+f(y)| \},\) x,y\(\in X\), with an \(0\leq \epsilon <1\) [cf. \textit{J. Tabor}, ibid. 35, 164-185 (1988; Zbl 0652.39013)]. It is shown that if X is a locally convex space and \(f:X\to {\mathbb{R}}\) is a discontinuous quasi-additive function, then the graph of f is dense in \(X\times {\mathbb{R}}\).
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 46A03
zbMATH DE Number: 4159320
zbMATH Keywords: locally convex space
zbMATH Keywords: discontinuous quasi-additive function
zbMATH Keywords: graph
reviewed by: Kazimierz Nikodem
MaRDI profile type: Publication
cites work: Q5804302
cites work: Q3218572
cites work: On functions behaving like additive functions
cites work: Quasi-additive functions
description: scientific article; zbMATH DE number 4159320