A fully pexiderized variant of d'Alembert's functional equations on monoids
type: Item
instance of: scholarly article
title: A fully pexiderized variant of d'Alembert's functional equations on monoids
zbMATH Open document ID: 1468.39011
published in: Results in Mathematics
publication date: 2021-06-23T00:00:00Z
review text: The functional equation \[f(xy)+g(\sigma(y)x)=h(x)k(y)\] in which \(f, g, h, k\) are complex-valued functions on groups or monoids generated by their squares and \(\sigma\) is an involutive automorphism is a pexiderization of both d'Alembert functional equations \(g(x+y)+g(x-y)=2g(x)g(y)\) and \(f(x+y)-f(x-y)=g(x)h(y)\) and a a variant of the Wilson functional equation \(f(x+y)+g(x-y)=h(x)k(y)\) for monoids. The author solves the above pexiderized functional equation. The special case of the equation when \(h = 2f\) was recently investigated by him in [Aequationes Math. 95, No. 2, 383--391 (2021; Zbl 1462.39021)]. Furthermore, he explores the continuous solutions on topological groups and monoids.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 7362283
zbMATH Keywords: involution
zbMATH Keywords: automorphism
zbMATH Keywords: d'Alembert's equations
zbMATH Keywords: monoid
zbMATH Keywords: topological monoid
zbMATH Keywords: Wilson's equations
author: Bruce Ebanks
MaRDI profile type: Publication
full work available at URL: s00025-020-01335-9
OpenAlex ID: W3119510395
cites work: Stability of a generalization of Wilson's equation
cites work: Some generalized quadratic functional equations on monoids
cites work: D'Alembert's other functional equation on monoids with an involution
cites work: A variant of Wilson's functional equation
cites work: A joint generalization of Van Vleck's and Kannappan's equations on groups
cites work: A functional equation on groups with involutions
cites work: A variant of d'Alembert's functional equation
DOI: 10.1007/S00025-020-01335-9
description: scientific article; zbMATH DE number 7362283