Ulam-Hyers-Rassias stability problem for several kinds of mappings
type: Item
instance of: scholarly article
title: Ulam-Hyers-Rassias stability problem for several kinds of mappings
zbMATH Open document ID: 1306.39023
author: Lahbib Oubbi
published in: Afrika Matematika
publication date: 2014-11-05T00:00:00Z
review text: Let \(f\) maps a (topological) vector space into a Banach space and let \(\alpha,\beta\) be given scalars. The stability of functional equations of the form \[ f(\alpha(x+y))+f(\beta(x-y))=(\alpha+\beta)f(x)+(\alpha-\beta)f(y) \] is considered. Namely, it is shown that if the above equation is satisfied approximately only (subject to precise definitions), then \(f\) is (in some sense) close to an additive (linear) mapping. Several earlier results can be derived as corollaries.
reviewed by: Jacek Chmieliński
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 6366022
zbMATH Keywords: Hyers-Ulam-Rassias stability
zbMATH Keywords: ring homomorphisms
zbMATH Keywords: \(n\)-derivations
MaRDI profile type: Publication
full work available at URL: s13370-012-0078-6
OpenAlex ID: W2080982645
cites work: On approximate ring homomorphisms
cites work: Approximately isometric and multiplicative transformations on continuous function rings
cites work: Q4822087
cites work: Approximately \(n\)-Jordan homomorphisms on Banach algebras
cites work: On the Stability of the Linear Functional Equation
cites work: Stability of functional equations in several variables
cites work: A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON
cites work: Remarks on the stability of additive functional equation
cites work: Extended Hyers–Ulam stability for Cauchy–Jensen mappings†
cites work: Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis
cites work: Functional Equations and Inequalities with Applications
cites work: Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
cites work: Hyers-Ulam-Rassias stability of generalized derivations
cites work: Q3649045
cites work: Stability of the Jensen-type functional equation in \(C^{\ast}\)-algebras: a fixed point approach
cites work: Q4470094
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: On the stability of functional equations and a problem of Ulam
cites work: On the stability of functional equations in Banach spaces
cites work: Q5511350
DOI: 10.1007/S13370-012-0078-6
description: scientific article; zbMATH DE number 6366022