Improvements on the stability of Euler-Lagrange type cubic maps in quasi-Banach spaces
type: Item
instance of: scholarly article
title: Improvements on the stability of Euler-Lagrange type cubic maps in quasi-Banach spaces
zbMATH Open document ID: 1499.39116
author: Yanyan Li
published in: Analysis Mathematica
publication date: 2022-03-16T00:00:00Z
review text: The main aim of this paper is to study the stability of the following linear functional equation, called the Euler-Lagrange type cubic functional equation: \[ f (ax + y) + f (x + ay) = (a + 1)(a - 1)^{2}[f (x) + f (y)] + a(a + 1)f (x + y).\] Here \(f\colon X\to Y\) denotes the unknown function and \(X\) is assumed to be a real quasi-normed space, while \(Y\) is a real quasi-Banach space and \(a\) is a fixed integer with \(a\notin \left\{-1, 0, 1 \right\}\). This problem has been formerly considered by \textit{K.-W. Jun} and \textit{H.-M. Kim} [J. Math. Anal. Appl. 332, No. 2, 1335--1350 (2007; Zbl 1117.39017)]. The main aim of this paper is to improve the above-mentioned results. Accordingly the authors answer the open question raised in the above paper, namely to investigate the stability of the above equation for the case \(r\) with \(-\log_{\vert a\vert}K_{Y}\leq r-3\leq \log_{\vert a\vert}K_{Y}\) and \(\vert a\vert >1\).
reviewed by: Eszter Gselmann
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 46A16
zbMATH DE Number: 7491539
zbMATH Keywords: Euler-Lagrange type cubic
zbMATH Keywords: functional equation
zbMATH Keywords: quasi-Banach space
MaRDI profile type: Publication
full work available at URL: s10476-021-0109-3
OpenAlex ID: W4200586157
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DOI: 10.1007/S10476-021-0109-3
description: scientific article; zbMATH DE number 7491539