In this paper, we study the eventual periodicity of the following fuzzy max-type difference equationwhere {α n } n 0 is a periodic sequence of positive fuzzy numbers and the initial values z −d , z −d+1 , . . . , z −1 are positive fuzzy numbers with d = max{m, r}. We show that if max(supp α n ) < 1, then every positive solution of this equation is eventually periodic with period 2m.

Let G be a graph and f : G → G be a continuous map. Denote by P (f ), R(f ), SA(f ) and U Γ(f ) the sets of periodic points, recurrent points, special α-limit points and unilateral γ-limit points of f , respectively. In this paper, we show that

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In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equationson an arbitrary time scale T with sup T = ∞, where n is a positive integer and δ = 1 or −1. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.

In this note, we consider the following rational difference equation:where f ∈ C((0, +∞) k , (0, +∞)) and g ∈ C((0, +∞) l , (0, +∞)) with k, l ∈ {1, 2, . . .}, 0 r 1 < · · · < r k and 0 m 1 < · · · < m l , and the initial values are positive real numbers. We give sufficient conditions under which the unique equilibrium x = 1 of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the recent literature.