Sentence examples for be decreasing on from inspiring English sources

then H ¯ ( x ) will be decreasing on [ a, b ].

Meanwhile, the Razumikhin-type technique has an advantage that the Lyapunov Krasovskii functional is not required to be decreasing on the whole state space.

Let a function (y:mathbb{N}_{a-1}rightarrowmathbb{R}) satisfy (y(a) leq0) and be decreasing on (mathbb{N}_{a}).

Let (theta: [0,1]rightarrow R) be continuous, and (theta'(t)) exist for (tin 0,1)) and be decreasing on ((0,1)).

Thus is decreasing on by Lemma 2.1.

Hence is decreasing on and is decreasing on by Lemma 2.1.

This leads to that is decreasing on by Lemma 2.1.

Hence is increasing on and is decreasing on by Lemma 2.1.

Let for we have that and is decreasing for so is decreasing for and is decreasing on by Lemma 2.2.

In order to prove that is decreasing on, assume on the contrary that for some.

Then (2.16) yields which is not possible because is decreasing on by (1.9) and (2.2).