Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments

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.