Unconditional convergence of difference equations
Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia (UNED), C/ Juan del Rosal 12, Madrid, 28040, Spain
Boundary Value Problems 2013, 2013:63 doi:10.1186/1687-2770-2013-63Published: 28 March 2013
We put forward the notion of unconditional convergence to an equilibrium of a difference equation. Roughly speaking, it means that can be constructed a wide family of higher order difference equations, which inherit the asymptotic behavior of the original difference equation. We present a sufficient condition for guaranteeing that a second-order difference equation possesses an unconditional stable attractor. Finally, we show how our results can be applied to two families of difference equations recently considered in the literature.