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Fixed points and stability in nonlinear neutral differential equations with variable delays
In this paper we use the contraction mapping theorem to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some previous results due to T. A. Burton , B. Zhang , Y. M. Dib, M. R. Maroun, Y. N. Raffoul . Two examples are also given to illustrate our work.