A note on the difference equation xn+1 = ∑i=0k αi /xn-ipi

Abstract

In this note we improve Theorem 2 in Ref. [3], about the difference equation x n+1 = ∑ i=0k α i /x n-ipi , n = 0,1,2,..., where k is a positive integer, α i ,p i ∈ (0, ∞) for i=0,...,k, and the initial conditions x -k , x -k+1 ,..., x 0 are arbitrary positive numbers.