A generalization of the Cosine-Sine functional equation on a semigroup
General Mathematics
2023-12-12 v1
Abstract
Given a semigroup equipped with an involutive automorphism , we determine the complex-valued solutions of the functional equation \begin{equation*}f(x\sigma(y))=f(x)g(y)+g(x)f(y)+h(x)h(y),\,\,x,y\in S,\end{equation*} in terms of multiplicative functions and solutions of the special cases of sine and cosine-sine functional equations.
Keywords
Cite
@article{arxiv.2312.05285,
title = {A generalization of the Cosine-Sine functional equation on a semigroup},
author = {Omar Ajebbar and Elhoucien Elqorach},
journal= {arXiv preprint arXiv:2312.05285},
year = {2023}
}