Sentence examples for elementary inequality from inspiring English sources

A set of criteria is presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals, introducing many parameters and combining with the elementary inequality technique.

In this Letter, several sufficient conditions are derived for the existence and uniqueness of periodic oscillatory solution for bi-directional associative memory (BAM) networks with time-varying delays by employing a new Lyapunov functional and an elementary inequality, and all other solutions of the BAM networks converge exponentially to the unique periodic solution.

By the elementary inequality (2.9).

Let be the elementary inequality (3.41).

We begin with an elementary inequality for real numbers.

By (4.13) and the following elementary inequality: (414).

Now we shall show two elementary inequalities in the following lemmas.

In this section we first represent some elementary inequalities and then we use these results to handle the nonlinear term.

In connection with work on the general theory of orthogonal series, Littlewood [1] raised some problems concerning elementary inequalities for infinite series.

Thanks to the standard results of linear theory presented in Section 2 and the elementary inequalities, we obtain the decay estimate of (1.9).

On the other hand, by applying the following two elementary inequalities [11]: (2.7). to the right-hand side of (2.6), we obtain (2.8).