Functions near some \((\alpha _1,\alpha _2)\)-double Jordan derivations in \(p\)-Banach algebras
type: Item
instance of: scholarly article
title: Functions near some \((\alpha _1,\alpha _2)\)-double Jordan derivations in \(p\)-Banach algebras
zbMATH Open document ID: 1382.39043
author: Ismail Nikoufar
published in: Bollettino dell'Unione Matematica Italiana
publication date: 2017-11-01T00:00:00Z
review text: \textit{M. Mirzavaziri} and \textit{E. O. Tehrani} [Bull. Iran. Math. Soc. 35, No. 1, 147--154 (2009; Zbl 1189.46058)] introduced an \((\alpha, \beta)\)-double derivation \(\alpha \circ \beta\) in a Banach algebra \(A\) for given linear derivations \(\alpha\) and \(\beta\) in \(A\). The author defines an \((\alpha, \beta)\)-double Jordan derivation \(f= \alpha \circ \beta\) in a Banach algebra \(A\) for given linear derivations \(\alpha\) and \(\beta\) in \(A\) as follows: \[ f(a^2 ) = f(a) a + a f(a) +\alpha(a)\beta(a) + \beta(a)\alpha(a) \] for all \(a\in A\), and proves the Hyers-Ulam stability of \((\alpha, \beta)\)-double Jordan derivations in Banach algebras. But there are some errors in the results: \(r<1\) in Theorem 2.6, \(r>1\) in Corollary 2.7, \(r>1\) in Theorem 2.8 and \(r>1\) in Corollary 2.9 are needed to obtain the correct results. The techniques and the ideas are so simple. The results are useful for beginners in the theory of functional inequalities and functional equations.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 6802154
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: \(p\)-Banach algebra
zbMATH Keywords: double Jordan derivation
zbMATH Keywords: derivation
zbMATH Keywords: additive functional equation
reviewed by: Choonkil Park
MaRDI profile type: Publication
full work available at URL: s40574-016-0074-0
OpenAlex ID: W2342783419
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DOI: 10.1007/S40574-016-0074-0
description: scientific article; zbMATH DE number 6802154