Stability of functional equations arising from number theory and determinant of matrices

Abstract

In this paper, we consider the Ulam–Hyers stability of the functional equations $$f(ux-vy,uy-vx)=f(x,y)f(u,v),$$ $$f(ux+vy,uy-vx)=f(x,y)f(u,v),$$ $$f(ux+vy,uy+vx)=f(x,y)f(u,v),$$ $$f(ux-vy,uy+vx)=f(x,y)f(u,v)$$ for all $x,y,u,v\in \mathbb{R}$, where $f:{\mathbb{R}}^2\to \mathbb{R}$, which arise from number theory and are connected with the characterizations of the determinant and permanent of two-by-two matrices.