Periodicity of a class of nonautonomous max-type difference equations

In this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x(n) = max{f(1)(x(n-k1), n), ... , f(m)(x(n-km), n),x(n-s)}, n is an element of N-0, and x(n) = min {f(1)(x(n-k1), n), ... , f(m)(x(n-km), n), x(n-s)}, n is an element of N-0, where 1 <= k(1) < ... < k(m); m; s is an element of N, and where the functions f(i) : (0, infinity) x N-0 -> (0, infinity), 1 <= i <= m, satisfy some additional conditions. These results considerably extend and unify numerous results on max-type difference equations existing in the literature. (C) 2011 Elsevier Inc. All rights reserved.