ON THE RECURSIVE SEQUENCE $x_{n+1}=\displaystyle\frac{A}{\prod^k_{i=0}x_{n-i}}+\displaystyle\frac{1}{\prod^{2(k+1)}_{j=k+2}x_{n-j}}$

Abstract

In [6] the authors proposed two open problems concerning the boundedness and the periodic nature of positive solutions of the nonlinear difference equation in the title. In this paper we prove a global covergence result and solve the open problems in the case $A \gt 1$.