A Solution Form of a Rational Difference Equation

Authors : Ramazan KARATAŞ

Pages : 20-23

View : 11 | Download : 9

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :This paper shows the solution form of the rational difference equation \\begin{equation*} x_{n+1}=\\frac{ax_{n-insert ignore into journalissuearticles values(2k+3);}}{-a\\mp x_{n-insert ignore into journalissuearticles values(k+1);}x_{n-insert ignore into journalissuearticles values(2k+3);}}\\text{ }% ,~n=0,1,... \\end{equation*} where $k$ is a positive integer $a$ and initial conditions are non-zero real numbers with $x_{n-insert ignore into journalissuearticles values(k+1);}x_{n-insert ignore into journalissuearticles values(2k+3);}\\neq \\mp a$ for all $n\\in N_{0}$.
Keywords : Rational difference equation, Solution, boundedness, periodicity