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Oscillation criteria for sublinear and superlinear first-order difference equations of neutral type with several delays

The purpose of this paper is to investigate the oscillatory behaviour of a class of first-order sublinear and superlinear neutral difference equations. Some conditions are established by applying Banach's Contraction mapping principle, Knaster-Tarski fixed point theorem and using several inequalities. We provide some examples to illustrate the outreach of the main results.