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In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation $${\Delta }^3(x_n+a_n{x}_{n-l}+b_n{x}_{n+m})+p_n{x}_{n-k}-q_n{x}_{n+r}=0,n\ge n_0$$ 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.