Generalized Hyers-Ulam stability of a general mixed additive-cubic functional equation in quasi-Banach spaces
type: Item
instance of: scholarly article
title: Generalized Hyers-Ulam stability of a general mixed additive-cubic functional equation in quasi-Banach spaces
zbMATH Open document ID: 1258.39016
author: Wan Xin Xu
author: Tian Zhou Xu
author: J. M. Rassias
publication date: 2012-11-07T00:00:00Z
review text: Let \(X\) and \(Y\) be real linear spaces. \textit{A. Najati} and \textit{G. Z. Eskandani} [J. Math. Anal. Appl. 342, No. 2, 1318--1331 (2008; Zbl 1228.39028)] have given the general solution \(f:X\to Y\) with \(f(0)=0\) of the functional equation \[ f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+2f(2x)-4f(x) \] and have proved its generalized Hyers-Ulam stability under the additional assumption that \(X\) is a quasi-normed space and \(Y\) is a \(p\)-Banach space. In this paper, the authors consider the above problems for the following more general equation \[ f(kx+y)+f(kx-y)=kf(x+y)+kf(x-y)+2f(kx)-2kf(x), \] where \(k\) is a fixed integer different from \(-1, 0\) and \(1\). The stability results are obtained by the direct method.
reviewed by: Krzysztof Ciepliński
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 6102830
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: additive mapping
zbMATH Keywords: cubic mapping
zbMATH Keywords: quasi-normed space
zbMATH Keywords: \(p\)-Banach space
MaRDI profile type: Publication
full work available at URL: s10114-011-9663-0
OpenAlex ID: W1985904831
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DOI: 10.1007/S10114-011-9663-0
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6102830