The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability oThe main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation xn+1 = α0xn + α1xn−l + α2xn−k ⁄ β0xn + β1xn−l + β2xn−k , n = 0, 1, 2, . . . where the coefficients αi , βi ∈ (0,∞) for i = 0, 1, 2, and l, k are positive integers. The initial conditions x−k, . . . , x−l , . . . , x−1, x0 are arbitrary positive real numbers such that l < k. Some numerical experiments are presented.
With the aid of the notion of weighted sharing and pseudo sharing of sets we prove three uniqueness results on meromorphic functions sharing three sets, all of which will improve a result of Lin-Yi in Complex Var. Theory Appl. (2003).