On the recursive sequence xn + 1 = max {c, frac(xnp, xn - 1p)}

Abstract

This work studies the boundedness and global attractivity for the positive solutions of the difference equation xn + 1 = max {c, frac(underover(x, n, p), underover(x, n - 1, p))}, n ∈ N0, with p, c ∈ (0, ∞). It is shown that: (a) there exist unbounded solutions whenever p ≥ 4, (b) all positive solutions are bounded when p ∈ (0, 4), (c) every positive solution is eventually equal to 1 when p ∈ (0, 4) and c ≥ 1, (d) all positive solutions converge to 1 whenever p, c ∈ (0, 1).