Difference Equations: An Improved Approach in Oscillation Theory

An equation which expresses a value of a sequence as a function of the other terms in the sequence is called a difference equation. Difference equation or discrete dynamical system is a very fascinating subject because we can derive much complex behavior based on simple formulation. some new oscillation criteria for first and third order neutral delay difference equation with positive and negative coefficients in the neutral term is obtained by utilizing summation average techniques and comparison principle. The aim of this study is to develop the new criteria for the oscillation so that we apply them when other criteria fails.