The Cosine-Sine functional equation on a semigroup with an involutive automorphism

被引：12

作者：

Ajebbar, Omar ^{[1
]}

Elqorachi, Elhoucien ^{[1
]}

机构：

[1] Ibn Zohr Univ, Fac Sci, Agadir, Morocco

来源：

AEQUATIONES MATHEMATICAE | 2017年 / 91卷 / 06期

关键词：

Semigroup; Cosine-Sine equation; Levi-Civita's equation; Involutive automorphism; Multiplicative function; Additive function;

D O I：

10.1007/s00010-017-0512-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine the complex-valued solutions of the following extension of the Cosine-Sine functional equation f(x sigma(y)) = f(x)g(y) + g(x)f(y) + h(x)h(y), x, y is an element of S, where S is a semigroup generated by its squares and is an involutive automorphism of S. We express the solutions in terms of multiplicative and additive functions.

引用

页码：1115 / 1146

页数：32

共 7 条

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