Asymptotic stability in totally nonlinear neutral difference equations
DOI:
https://doi.org/10.4067/S071609172015000300005Keywords:
Fixed point, Stability, Neutral difference equations, Variable delay.Abstract
In this paper we use fixed point method to prove asymptotic stability results of the zero solution of the totally nonlinear neutral difference equation with variable delay
∆ x (n) = —a (n) f (x (n — τ (n))) + ∆g (n, x (n — τ (n))).
An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Raffoul (2006) , Yankson (2009), Jin and Luo (2009) and Chen (2013).
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