Solution of Hyers-Ulam stability problem for generalized Pappus' equation
type: Item
instance of: scholarly article
title: Solution of Hyers-Ulam stability problem for generalized Pappus' equation
zbMATH Open document ID: 1070.39029
author: Kil-Woung Jun
author: Hark-Mahn Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: The authors generalize the famous Pappus' identity and introduce a new functional equation \[ n^2 f(x+my) + mnf(x-my) = (m+n)(nf(x) + mf(ny)) \tag \(*\) \] for given positive integers \(m\) and \(n\). By applying the direct method, they prove the Hyers-Ulam-Rassias stability of the equation (\(*\)) for a class of functions \(f : X \to Y\), where \(X\) is a vector space and \(Y\) is a Banach space.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 2141769
zbMATH Keywords: Hyers-Ulam-Rassias stability
zbMATH Keywords: Pappus' equation
zbMATH Keywords: quadratic mapping
zbMATH Keywords: direct method
zbMATH Keywords: vector space
zbMATH Keywords: Banach space
zbMATH Keywords: functional equation
reviewed by: Soon-Mo Jung
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.06.008
OpenAlex ID: W2091440797
cites work: Q3992445
cites work: Remarks on the stability of functional equations
cites work: On the stability of the quadratic mapping in normed spaces
cites work: Q4879432
cites work: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
cites work: Stability of Isometries
cites work: On the Stability of the Linear Functional Equation
cites work: On the asymptoticity aspect of Hyers-Ulam stability of mappings
cites work: Approximate homomorphisms
cites work: On the Hyers-Ulam-Rassias stability of a pexiderized quadratic inequality
cites work: Q4012607
cites work: Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: On the stability of functional equations in Banach spaces
cites work: Q5511350
DOI: 10.1016/J.JMAA.2004.06.008
Recommended article: A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation
Recommended article: ON HYERS-ULAM STABILITY OF THE PEXIDER EQUATION
Recommended article: The Hyers-Ulam-Rassias stability of the pexiderized equations
Recommended article: Hyers-Ulam stability of a general linear partial differential equation
Recommended article: On Hyers-Ulam-Rassias stability of the Pexider equation
Recommended article: Hyers-Ulam stability of the Pexider equation
Recommended article: Q5699773
Recommended article: Q5743707
Recommended article: Hyers--Ulam--Rassias stability of a generalized Pexider functional equation
Recommended article: Q5409422
description: scientific article; zbMATH DE number 2141769