Solution of several functional equations on nonunital semigroups using Wilson's functional equations with involution
type: Item
instance of: scholarly article
title: Solution of several functional equations on nonunital semigroups using Wilson's functional equations with involution
zbMATH Open document ID: 1412.39025
DOI: 10.1155/2014/463918
author: Prasanna Sahoo
author: Jaeyoung Chung
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Let \(S\) be a nonunital commutative semigroup, \(\sigma\colon S \to S\) an involution, and \(\mathbb{C}\) the set of complex numbers. In this paper, first we determine the general solutions \(f, g\colon S \to \mathbb{C}\) of Wilson's generalizations of d'Alembert's functional equations \(f(x + y) + f(x + \sigma y) = 2 f(x) g(y)\) and \(f(x + y) + f (x + \sigma y) = 2 g(x) f(y)\) on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 7022431
Wikidata QID: Q59038462
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/463918
OpenAlex ID: W2123304375
cites work: Q4817090
cites work: Functional Equations on Groups
cites work: Functional equations on semigroups
cites work: Q5840739
cites work: Über eine Lösungsmethode gewisser Funktionalgleichungen
cites work: On a Quadratic-Trigonometric Functional Equation and Some Applications
cites work: D'Alembert's and Wilson's functional equations for vector and $2\times 2$ matrix valued functions
cites work: Q3992445
cites work: On solutions of the second generalization of d'Alembert's functional equation on a restricted domain
cites work: Q3905871
cites work: Wilson's functional equation on \(P_3\)-groups
cites work: Q5201017
cites work: d'Alembert's and Wilson's equations on Lie groups
cites work: Q3653821
cites work: Wilson’s functional equation in algebras
cites work: Functional equations on abelian groups with involution
cites work: Q4894694
description: scientific article; zbMATH DE number 7022431