Nearly quadratic \(n\)-derivations on non-Archimedean Banach algebras
type: Item
instance of: scholarly article
title: Nearly quadratic \(n\)-derivations on non-Archimedean Banach algebras
zbMATH Open document ID: 1248.39033
DOI: 10.1155/2012/961642
author: Badrkhan Alizadeh
author: Gwang Hui Kim
author: Young Whan Lee
author: Madjid Eshaghi Gordji
published in: Discrete Dynamics in Nature and Society
publication date: 2012-08-14T00:00:00Z
review text: Summary: Let \(n > 1\) be an integer, let \(A\) be an algebra, and \(X\) be an \(A\)-module. A quadratic function \(D : A \rightarrow X\) is called a quadratic \(n\)-derivation if \(D(\prod^n_{i=1} a_i) = D(a_1) a^2_2 \cdots a^2_n + a^2_1 D(a_2) a^2_3 \cdots a^2_n + \cdots + a^2_1 a^2_2 \cdots a^2_{n-1} D(a_n)\) for all \(a_1, \dots, a_n \in A\). We investigate the Hyers-Ulam stability of quadratic \(n\)-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 46J10
zbMATH DE Number: 6065462
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: quadratic \(n\)-derivations
zbMATH Keywords: non-Archimedean Banach algebras
zbMATH Keywords: non-Archimedean Banach modules
zbMATH Keywords: Banach fixed point theorem
Wikidata QID: Q58700893
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/961642
OpenAlex ID: W2094394438
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description: scientific article; zbMATH DE number 6065462