On Hyers-Ulam stability of Hosszú's functional equation
type: Item
instance of: scholarly article
title: On Hyers-Ulam stability of Hosszú's functional equation
zbMATH Open document ID: 0828.39019
DOI: 10.1007/BF03323041
author: Costanza Borelli
published in: Results in Mathematics
publication date: 1996-01-11T00:00:00Z
review text: Let \(Hf(x, y):= f(x+ y- xy)+ f(xy)- f(x)- f(y)\). The following result on Hyers-Ulam stability of the Hosszú equation \(Hf(x, y)= 0\) is proved: Let \(f: \mathbb{R}\to \mathbb{R}\) be a function satisfying \(|Hf(x, y)|\leq \delta\) for some \(\delta> 0\). There exists an additive function \(a: \mathbb{R}\to \mathbb{R}\) such that the difference \(f- a\) is bounded iff the even part \(h\) of \(f\) satisfies \(|Hh(x, y)|\leq \varepsilon\) for some \(\varepsilon> 0\).
Mathematics Subject Classification ID: 39B72
zbMATH DE Number: 785163
zbMATH Keywords: Hosszú's functional equation
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: additive function
reviewed by: Kazimierz Nikodem
MaRDI profile type: Publication
cites work: The complete solution of Hosszu's functional equation over a field
cites work: The stability of homomorphisms and amenability, with applications to functional equations
cites work: On the Stability of the Linear Functional Equation
description: scientific article; zbMATH DE number 785163