On the Difference Equation 𝑥𝑛+1=𝛼+𝑥𝑛−𝑚/𝑥𝑘𝑛

Abstract

We investigate the global behaviour of the difference equation of higher order 𝑥𝑛+1=𝛼+𝑥𝑛−𝑚/𝑥𝑘𝑛, 𝑛=0,1,…, where the parameters 𝛼,𝑘∈(0,∞) and the initial values 𝑥−𝑚,𝑥−(𝑚−1),…,𝑥−2,𝑥−1, and 𝑥0 are arbitrary positive real numbers.