Global Behavior of the Max‐Type Difference Equation<i>x</i>_<i>n</i>+1= max {1/<i>x</i>_<i>n</i>,<i>A</i>_<i>n</i>/<i>x</i>_<i>n</i>−1}

Abstract

We study global behavior of the following max‐type difference equation x n +1 = max {1/ x n , A n / x n −1 }, n = 0, 1, …, where is a sequence of positive real numbers with 0 ≤ inf A n ≤ sup A n &lt; 1. The special case when is a periodic sequence with period k and A n ∈ (0, 1) for every n ≥ 0 has been completely investigated by Y. Chen. Here we extend his results to the general case.