Abstract
In this paper we use fixed point method to prove asymptotic stability results of the zero solution of a nonlinear neutral difference equation with variable delay. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Raffoul (J Math Anal Appl 324:1356–1362 2006), Yankson (Electron J Qual Theory Differ Equ 8:1–7 2009), Jin and Luo (Georgian Math J 16:683–691 2009) and Chen (A fixed point approach towards stability of delay differential equations with applications to neural networks 2013).
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