The generalized hyperstability of general linear equations in quasi-Banach spaces
type: Item
instance of: scholarly article
title: The generalized hyperstability of general linear equations in quasi-Banach spaces
zbMATH Open document ID: 1391.39033
author: Nguyen Van Dung
author: Vo Thi Le Hang
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-05-31T00:00:00Z
review text: The stability aspects of the general linear equation \(f(ax+by)=Af(x)+Bf(y)\) have been studied intensively. However, as the authors of the present paper point out, some of the recent results may not hold in arbitrary normed spaces. These approaches replace the original space by its completion, which may cause problems when applying fixed point methods. Motivated by this fact, the authors investigate the hyperstability of the above linear equation in quasi-Banach spaces instead of normed spaces. The key tool of the proofs is an extension of the fixed point result of \textit{J. Brzdęk} et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6728--6732 (2011; Zbl 1236.39022)] to \(b\)-metric spaces.
reviewed by: Mihály Bessenyei
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6877114
zbMATH Keywords: fixed point
zbMATH Keywords: quasi-Banach space
zbMATH Keywords: hyperstability
zbMATH Keywords: general linear equation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.01.070
OpenAlex ID: W2791945371
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DOI: 10.1016/J.JMAA.2018.01.070
description: scientific article; zbMATH DE number 6877114