EXISTENCE OF NONOSCILLATORY SOLUTIONS TO FIRST ORDER NEUTRAL TYPE DIFFERENCE EQUATIONS WITH MIXED ARGUMENTS

Abstract

In this paper, the authors present some sufficient conditions for the existence of nonoscillatory solutions to following first order neutral type difference equation

∆(x_n + a_n x_{n−l} + b_n x_{n+m}) + p_n x_{n−k} − q_n x_{n+r}= 0, n ≥ n0

having both delay and advanced terms via Banach contraction principle. Examples are provided to illustrate the results. The results obtained in this paper generalized some of the existing results.