This paper shows that every well-defined solution of the following max-type difference equationwhere A ∈ R and the initial conditions x −2 , x −1 , x 0 are arbitrary non-zero real numbers is eventually periodic with period three by using new iteration method for the more general nonlinear difference equations and inequality skills as well as the mathematical induction. Our main results considerably improve results appearing in the literature.

Our aim in this paper is to investigate the dynamics of a third-order fuzzy difference equation. By using new iteration method for the more general nonlinear difference equations and inequality skills as well as a comparison theorem for the fuzzy difference equation, some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for the nonlinear fuzzy system are obtained. Moreover, some numerical solutions of the equation describing the system are given to verify our theoretical results.