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Open Access Research

Unconditional convergence of difference equations

Daniel Franco and Juan Peran*

Author Affiliations

Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia (UNED), C/ Juan del Rosal 12, Madrid, 28040, Spain

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Boundary Value Problems 2013, 2013:63  doi:10.1186/1687-2770-2013-63

Published: 28 March 2013

Abstract

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.

MSC: 39A11.

Keywords:
difference equations; global asymptotic stability