The sine addition and subtraction formulas on semigroups
type: Item
instance of: scholarly article
title: The sine addition and subtraction formulas on semigroups
zbMATH Open document ID: 1488.39065
published in: Acta Mathematica Hungarica
publication date: 2021-08-03T00:00:00Z
review text: The functional equation \(f(xy) = f(x)g(y)+g(x)f(y),\,\, x,y \in S\) is called the sine addition formula on a semigroup \(S\). Several mathematicians have investigated its solutions on groups, regular semigroups, and semigroups which are generated by their squares. In the paper the author finds the general solution on all semigroups using a transfinite induction argument. In addition, he presents the general solution of the sine subtraction formula \(f(x\sigma(y))=f(x)g(y) - g(x)f(y)\) on monoids, where \(\sigma\) is an automorphic involution. He also gives the general continuous solutions on topological semigroups.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 7377606
zbMATH Keywords: semigroup
zbMATH Keywords: prime ideal
zbMATH Keywords: topological semigroup
zbMATH Keywords: sine addition formula
zbMATH Keywords: sine subtraction formula
zbMATH Keywords: monoid
author: Bruce Ebanks
MaRDI profile type: Publication
full work available at URL: s10474-021-01149-3
OpenAlex ID: W3167974152
Wikidata QID: Q113904568
cites work: Q5514010
cites work: Q3992445
cites work: A generalization of the cosine-sine functional equation on groups
cites work: D'Alembert's other functional equation on monoids with an involution
cites work: Functional Equations on Groups
cites work: Q5330937
DOI: 10.1007/S10474-021-01149-3
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description: scientific article; zbMATH DE number 7377606