Asymptotic Behavior of Solutions of Nonautonomous Difference Equations

In this paper we present a theorem on asymptotic behavior of W(n, x(n)) where x(n) is a solution of the difference equation x(n+1)=ƒ(n, x(n)), nϵN+ and W(n, x):N+ × Rd→R+ is continuous. As applications we discuss examples which cannot be handled by the discrete LaSalle′s invariance principle and the discrete Salvadori′s theorem