Let ; be an independent sequence of real-valued matrices and f(n,x) be an valued mapping defined on . The author investigates various definitions of the stability of the solutions of the equation
A typical result is the following: Let us suppose that
Then for any positive there exists a positive () such that for any n one has provided that
An other kind of result is the following: Let us suppose that
Analogous results hold for the -norm and various conditions on the behavior of the products of the matrices and contraction properties of the function f.