Scholarlink

Given a semigroup S generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations \(\displaystyle \begin{aligned} \begin {array}{l}f(xy)=f(x)g_{1}(y)+g_{1}(x)f(y)+\lambda _{1}^{2}\,h(x)h(y),\; x,y\in S,\\ h(xy)=h(x)g_{2}(y)+g_{2}(x)h(y)+\lambda _{2}^{2}\,f(x)f(y),\; x,y\in S, \end {array} \end{aligned} \) where \(\lambda _{1},\lambda _{2}\in \mathbb {C}\) are given constants and \(f,g_{1},g_{2},h:S\to \mathbb {C}\) are unknown functions.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A System of Cosine-Sine Functional Equations on a Semigroup Generated by Its Squares

  • 章节

  • 发表日期：

    2026年

查看全文
  • Ajebbar Omar,
  • Elqorachi Elhoucien

摘要

Given a semigroup S generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations \(\displaystyle \begin{aligned} \begin {array}{l}f(xy)=f(x)g_{1}(y)+g_{1}(x)f(y)+\lambda _{1}^{2}\,h(x)h(y),\; x,y\in S,\\ h(xy)=h(x)g_{2}(y)+g_{2}(x)h(y)+\lambda _{2}^{2}\,f(x)f(y),\; x,y\in S, \end {array} \end{aligned} \) where \(\lambda _{1},\lambda _{2}\in \mathbb {C}\) are given constants and \(f,g_{1},g_{2},h:S\to \mathbb {C}\) are unknown functions.