Solution and stability of a cubic functional equation
type: Item
instance of: scholarly article
title: Solution and stability of a cubic functional equation
zbMATH Open document ID: 1201.39024
author: Kil-Woung Jun
author: Sang-Baek Lee
author: Won-Gil Park
publication date: 2010-09-22T00:00:00Z
review text: Similar to the method used by \textit{H.-Y Chu} and \textit{D.-S. Kang} [J. Math. Anal. Appl. 325, No.~1, 595--607 (2007; Zbl 1106.39025)] and \textit{A. Najati} and \textit{Ch. Park} [Acta Math. Sin., Engl. Ser. 24, No.~12, 1953--1964 (2008; Zbl 1159.39014)], the authors obtain the general solution and investigate the stability of the following cubic functional equation \[ f(x+ny)+f(x-ny)+f(nx)=n^2f(x+y)+n^2f(x-y)+(n^3-2n^2+2)f(x), \] where \(n\geq 2\) is an integer and \(f\) is a map between real vector spaces. They also investigate the stability of the equation above by using the fixed point method.
reviewed by: Maryam Amyari
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5790099
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: cubic functional equation
zbMATH Keywords: alternative of fixed point
MaRDI profile type: Publication
full work available at URL: s10114-010-8621-6
OpenAlex ID: W2008825236
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DOI: 10.1007/S10114-010-8621-6
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5790099