On the stability of nonautonomous difference equations

Memarbashi, Reza

doi:10.1080/10236190701859559

Cited by 5 publications

(1 citation statement)

References 9 publications

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“…For X = R Lemma 1 is also implied by Theorem 2 in [15] where Memarbashi uses a contraction argument adapted from Theorem 3 in [20] (exponential stability, autonomous case in R). Contraction arguments with their geometric flavor are intuitively appealing and they also work for nonexponential asymptotic stability; see [20] for the autonomous case and [16] which extends the result in [20] to certain non-autonomous equations.…”

Section: General Results On Convergencementioning

confidence: 94%

Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

Sedaghat

2013

Journal of Difference Equations and Applications

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Non-autonomous, higher order difference equations of type! with real variables and parameters have appeared frequently in the literature. These equations are well defined on Banach algebras, and existing convergence results can be generalized from real numbers to algebras. Through this generalization and by using a recently obtained semiconjugate factorization of the above equation, new sufficient conditions are obtained for the convergence to zero of all solutions of nonlinear difference equations of the above type. Where reduction of order is possible, these conditions extend the ranges of parameters for which the origin is a global attractor even in the case of real variables and parameters.

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