A VARIANT OF D'ALEMBERT'S AND WILSON'S FUNCTIONAL EQUATIONS FOR MATRIX VALUED FUNCTIONS

被引：0
|
作者：
Chahbi, Abdellatif [1 ]
Chakiri, Mohamed [1 ]
Elqorachi, Elhoucien [1 ]
机构：
[1] Ibn Zohr Univ, Fac Sci, Dept Math, Equipe Equat Fonct & Applicat, Agadir, Morocco
来源：
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 39卷 / 03期
关键词：
Topological group; monoid; D'Alembert's equation; Wilson's equation; matrix; automorphism; involution; VECTOR;
D O I：
10.4134/CKMS.c220073
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given M a monoid with a neutral element e . We show that the solutions of d'Alembert's functional equation for n x n matrices Phi(pr, qs) + Phi (sp, rq) = 2 Phi(r, s)Phi(p, q), p, q, r, s is an element of M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation {f(pr, qs) + f(sp, rq) = 2 Phi(r, s)f(p, q), {Phi(p, q) = Phi(q, p), p, q, r, s is an element of M are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3 .
引用
收藏
页码：785 / 802
页数：18
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