Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Oscillation of a Class of Third Order Generalized Functional Difference Equation

Version 1 : Received: 27 December 2018 / Approved: 28 December 2018 / Online: 28 December 2018 (12:37:29 CET)

How to cite: Mohan Reddy, P.; Kilicman, A.; Manuel, M.S. Oscillation of a Class of Third Order Generalized Functional Difference Equation. Preprints 2018, 2018120349 (doi: 10.20944/preprints201812.0349.v1). Mohan Reddy, P.; Kilicman, A.; Manuel, M.S. Oscillation of a Class of Third Order Generalized Functional Difference Equation. Preprints 2018, 2018120349 (doi: 10.20944/preprints201812.0349.v1).

## Abstract

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form $${\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0,$$ where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

## Keywords

Generalized difference operator; Oscillation; Convergence.

## Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

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