A note on mutual stability
The author in this short note discusses the problem of mutual stability of solutions to two difference equations of the type \[ x(k+1)=f \bigl(x(k), k\bigr) \] and \[ y(k+1)= g\bigl(y(k), k\bigr). \] Any two solutions \(x (k)= x(k,x_0)\) and \(y(k)= y(k,y_0)\) \((k\in\mathbb{Z}^+)\) with initial conditions \(x(0)= x_0\) and \(y(0)=y_0\) are said to be mutually stable, if for each \(\varepsilon > 0\) there exists a \(\delta>0\), such that \(\|x_0-y_0 \|\leq\delta\) implies \(\|x(k)-y(k) \|< \varepsilon\) for \(k\in\mathbb{Z}^+\).
scientific article; zbMATH DE number 1371677