On a nonlinear generalized max-type difference equation

The boundedness character of positive solutions of the following max-type difference equationxn=max{A,xn−1pxn−kr},n∈N0, where k∈N∖{1}k∈N∖{1}, the parameters A and r are positive and p is a nonnegative real number is studied in this paper. Our main results considerably improve results appearing in the literature.