A system of cosine-sine functional equations on a semigroup generated by its squares
Functional Analysis
2022-09-21 v1
Abstract
Given a semigroup 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)+\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{align*} where are given constants and are unknown functions.
Keywords
Cite
@article{arxiv.2209.09571,
title = {A system of cosine-sine functional equations on a semigroup generated by its squares},
author = {Omar Ajebbar and Elhoucien Elqorachi},
journal= {arXiv preprint arXiv:2209.09571},
year = {2022}
}