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Furthermore, Corollary 3.1 guarantees that ( X 2, q G 2 ) is left/right-Cauchy and left/right-convergent.

The Corollary 1 can be straightforwardly derived via Theorem 1. Furthermore, Corollary 1 reveals a flexible method to switch between time domain and frequency domain with special modulation orders controlling.

Furthermore, Corollary 1 and Theorem 2 imply that all solutions of System (2) converge to an equilibrium or minimal period-two solutions, and since, by Theorem 6, E 0 is a repeller, all solutions converge to E + (which is, in view of Theorem 7, locally asymptotically stable) or minimal period-two solutions (14).

Furthermore, by Corollary 3.3, the linear differential equation (18) has the generalized Hyers-Ulam stability.

Furthermore, from Corollary 26, we obtain exactly the fixed point for Kannan mappings given in [4], i.e., Theorem 4 in Section 1.

Furthermore, using Corollary 4.2, we know that the limit of b-bistochasticity converges to a fixed point, thus we need to consider several cases.

Furthermore, by Corollary 3.2, one can see that ∑ k = 1 N sup x ∈ S | a ( f, λ k, x ) | 2 ≤ M 2. Thus, there is a countable set of real numbers Λ such that a f, λ, x) ≡ 0 on S if λ ∉ Λ.

Furthermore as corollaries, we obtain recent results of Rezapour and Hamlborani (2008).

Furthermore, as corollaries, the corresponding conclusion is provided to ensure the delayed Cohen Grossberg neural networks without reaction-diffusion term can reach fixed-time synchronization goal.

Furthermore, by Corollaries 2.2 and 2.4, we can get the following important Chungtype strong law of large numbers for arrays of rowwise NOD random variables.

Furthermore, choosing in Corollary 2.7, we get the following result.