On the Recursive Sequence xn=A+xn−kpxn−1r

الملخص EN

This paper studies the dynamic behavior of the positive solutions to the difference equation xn=A+xn−kp/xn−1r, n=1,2,…, where A,p, and r are positive real numbers, and the initial conditions are arbitrary positive numbers.

We establish some results regarding the stability and oscillation character of this equation for p∈(0,1).