ϕ0ϕ0-boundedness and practical ϕ0ϕ0-stability of difference equations

In this paper, we develop the notions of ϕ0ϕ0-boundedness and practical ϕ0ϕ0-stability for difference equations via perturbing cone-valued Lyapunov functions, and obtain sufficient conditions of ϕ0ϕ0-boundedness and practical ϕ0ϕ0-stability.