# Article

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Keywords:
third order; nonoscillation; delay and advanced arguments; neutral difference equation
Summary:
In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation $$\Delta ^3(x_n+a_n x_{n-l} +b_n x_{n+m})+p_n x_{n-k} - q_n x_{n+r}=0,\quad n\geq n_0$$ via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing results.
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