Stability and superstability of generalized \((\theta, \phi)\)-derivations in non-Archimedean algebras: fixed point theorem via the additive Cauchy functional equation
type: Item
instance of: scholarly article
title: Stability and superstability of generalized \((\theta, \phi)\)-derivations in non-Archimedean algebras: fixed point theorem via the additive Cauchy functional equation
zbMATH Open document ID: 1238.39011
DOI: 10.1155/2011/726020
author: Gwang Hui Kim
author: Badrkhan Alizadeh
author: M. B. Ghaemi
author: Madjid Eshaghi Gordji
published in: Journal of Applied Mathematics
publication date: 2012-04-04T00:00:00Z
review text: Summary: Let \(A\) be an algebra, and let \(\theta, \phi\) be ring automorphisms of \(A\). An additive mapping \(H : A \rightarrow A\) is called a \((\theta, \phi)\)-derivation if \(H(xy) = H(x)\theta(y) + \phi(x)H(y)\) for all \(x, y \in A\). Moreover, an additive mapping \(F : A \rightarrow A\) is said to be a generalized \((\theta, \phi)\)-derivation if there exists a \((\theta, \phi)\)-derivation \(H : A \rightarrow A\) such that \(F(xy) = F(x)\theta(y) + \phi(x)H(y)\) for all \(x, y \in A\). In this paper, we investigate the superstability of generalized \((\theta, \phi)\)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy's functional equation.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 6021619
zbMATH Keywords: ring automorphisms
zbMATH Keywords: derivation
zbMATH Keywords: superstability
zbMATH Keywords: non-Archimedean algebras
zbMATH Keywords: fixed point theorem
zbMATH Keywords: Cauchy's functional equation
Wikidata QID: Q58690502
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/726020
OpenAlex ID: W2108904008
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description: scientific article; zbMATH DE number 6021619