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.
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页码：1 / 14
页数：14
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