On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules.
type: Item
instance of: scholarly article
title: On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules.
zbMATH Open document ID: 1046.39023
author: Choonkil Park
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-03-14T00:00:00Z
review text: Let \(X,Y\) be Banach modules over a Banach \(\ast\)-algebra \(A\). A mapping \(Q:X\to Y\) is called \(A\)-quadratic if it satisfies \[ Q(x+y)+Q(x-y)=2Q(x)+2Q(y)\quad \text{and}\quad Q(ax)=aQ(x)a^{\ast} \] for all \(a\in A\), \(x,y\in X\). Two types of generalized \(A\)-quadratic mappings are considered and for both of them the stability is proved. The research was motivated by the stability results for the quadratic equation obtained by \textit{F. Skof} [Rend. Semin. Mat. Fis. Milano 53, 113--129 (1983; Zbl 0599.39007)], \textit{P. W. Cholewa} [Aequationes Math. 27, 76--86 (1984; Zbl 0549.39006)] and \textit{S. Czerwik} [Abh. Math. Semin. Univ. Hamb. 62, 59--64 (1992; Zbl 0779.39003)] as well as by some ideas of \textit{Th. M. Rassias}.
reviewed by: Jacek Chmieliński
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 46H25
zbMATH DE Number: 2056506
zbMATH Keywords: generalized \(A\)-quadratic mappings
zbMATH Keywords: stability
zbMATH Keywords: Banach modules
zbMATH Keywords: Banach \(\ast\)-algebra
zbMATH Keywords: quadratic functional equation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.10.027
OpenAlex ID: W2036347655
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DOI: 10.1016/J.JMAA.2003.10.027
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description: scientific article; zbMATH DE number 2056506