The cosine-sine functional equation on a semigroup with an involutive automorphism
type: Item
instance of: scholarly article
title: The cosine-sine functional equation on a semigroup with an involutive automorphism
zbMATH Open document ID: 1385.39004
author: Omar Ajebbar
author: E. Elqorachi
published in: Aequationes Mathematicae
publication date: 2018-01-12T00:00:00Z
review text: The authors investigate the functional equation \[ f(x\sigma(y))=f(x)g(y)+g(x)f(y)+h(x)h(y), \quad x,y \in S,\tag{E} \] where \(S\) is a semigroup generated by its quares and \(\sigma\) is an involutive automorphism of \(S\). This functional equation is a generalization of sine and cosine addition laws and is a special Levi-Civta equation. The main result of the paper gives the form of the solutions of equation (E), where \(f\), \(g\) and \(h\) are complex-valued functions, in term of multiplicative and additive functions. Different treatment is required whether the functions \(f\) and \(h\) are lineraly dependent or independent.
reviewed by: Gian Luigi Forti
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39B42
zbMATH DE Number: 6825377
zbMATH Keywords: semigroup
zbMATH Keywords: cosine-sine equation
zbMATH Keywords: Levi-Civita functional equation
zbMATH Keywords: involutive automorphism
zbMATH Keywords: multiplicative function
zbMATH Keywords: additive function
MaRDI profile type: Publication
full work available at URL: s00010-017-0512-9
OpenAlex ID: W2762629014
cites work: Q5514010
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cites work: Q5806876
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cites work: Functional Equations on Groups
DOI: 10.1007/S00010-017-0512-9
description: scientific article; zbMATH DE number 6825377