论文标题
其正方形生成的半群上的余弦函数方程系统
A system of cosine-sine functional equations on a semigroup generated by its squares
论文作者
论文摘要
给定的半群$ s $由其正方形生成，我们确定以下余弦函数方程式的复杂值解决方案\ begin \ begin {align*} f（xy）= f（x）g_ {1}（y）（y）+g_ {y）+g_ {1}+g_ {1}（x）f（y）+λ____________{1}^y {y}^2}^{2} x，y \ in s，\\ h（xy）= h（x）g_ {2}（y）+g_ {2}（x）h（y）+λ_{2}^{2}^{2} \，f（x）f（x）f（y），\; x，y \ in s，\ end {align*}其中$λ_{1}，λ_{2} \ in \ mathbb {c} $被赋予常数，$ f，g_ {1}，g_ {1}，g_ {2}，h：s \ to \ to \ to \ to \ to \ to \ to \ to \ to \ mathbb {c} $ neshone undain nothing函数。
Given a semigroup $S$ generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations \begin{align*} f(xy)=f(x)g_{1}(y)+g_{1}(x)f(y)+λ_{1}^{2}\,h(x)h(y),\; x,y\in S,\\ h(xy)=h(x)g_{2}(y)+g_{2}(x)h(y)+λ_{2}^{2}\,f(x)f(y),\; x,y\in S, \end{align*} where $λ_{1},λ_{2}\in\mathbb{C}$ are given constants and $f,g_{1},g_{2},h:S\to\mathbb{C}$ are unknown functions.
