Stability of the Cosine-Sine Functional Equation on amenable groups

TL;DR

This paper investigates the stability of a specific cosine-sine functional equation within the context of amenable groups, providing insights into its behavior and solutions under perturbations.

Contribution

It establishes the stability of a complex functional equation on amenable groups, extending previous stability results to a broader algebraic setting.

Findings

Proves stability of the functional equation on amenable groups

Characterizes solutions under approximate conditions

Extends stability theory to new functional equations

Abstract

In this paper we establish the stability of the functional equation \begin{equation*}f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y),\;x,y\in G,\end{equation*} where $G$ is an amenable group.