A VARIANT OF D'ALEMBERT'S FUNCTIONAL EQUATION ON SEMIGROUPS WITH ENDOMORPHISMS

被引：3

作者：

Akkaoui, Ahmed ^{[1
]}

El Fatini, Mohamed ^{[1
]}

Fadli, Brahim ^{[2
]}

机构：

[1] Ibn Tofail Univ, Fac Sci, Dept Math, BP 14000, Kenitra, Morocco

[2] Chouaib Doukkali Univ, Fac Sci, Dept Math, BP 24000, El Jadida, Morocco

来源：

ANNALES MATHEMATICAE SILESIANAE | 2022年 / 36卷 / 01期

关键词：

functional equation; d'Alembert; semigroup; multiplicative function; endomorphism;

D O I：

10.2478/amsil-2022-0004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S be a semigroup, and let phi, psi: S -> S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d'Alembert's functional equation f(x phi(y)) + f(psi(y)x) = 2f(x)f(y), x,y is an element of S, where f : S -> C is the unknown function by expressing its solutions in terms of multiplicative functions. Some consequences of this result are presented.

引用

页码：1 / 14

页数：14

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