A Solution Form of A Higher Order Difference Equation

Year 2021, Volume: 9 Issue: 2, 316 - 323, 15.10.2021

Ramazan Karataş , Ali Gelişken

Abstract

The main aim of this paper is to investigate the solutions of the difference equation \[ x_{n+1}=\frac{(-1)^{n}ax_{n-2k}}{a+(-1)^{n}\prod\limits_{i=0}^{2k}x_{n-i}% }\text{ },~n=0,1,... \] where $k$ is a positive integer and initial conditions are non zero real numbers with $\prod\limits_{i=0}^{2k}x_{n-i}\neq\mp a.$

Keywords

Difference equation, Solutions, Boundedness, periodicity

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