On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i)

Abstract

The main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number.