On the difference equation x n = x n-k/b+cx n-1 ⋯ x n-k

Abstract

We describe the behavior of well-defined solutions of the difference equationx n=x n-kb+cx n-1⋯x n-k,n∈N 0,where k∈ℕ, parameters b, c and the initial values x -k,⋯, x -1) are real numbers. These results, among others, improve and extend our results in [S. Stević, More on a rational recurrence relation, Appl. Math. E-Notes 4 (2004) 80-85].