The stability of a Cosine-Sine Functional Equation on abelian groups

TL;DR

This paper investigates the stability of a specific cosine-sine functional equation on abelian groups, providing conditions under which solutions are stable and close to exact solutions.

Contribution

It establishes the stability of a particular cosine-sine functional equation on abelian groups, extending the understanding of functional equation stability in algebraic structures.

Findings

Proved stability conditions for the functional equation.

Identified bounds for approximate solutions.

Extended stability results to abelian groups.

Abstract

In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.