Sentence examples for absolutely function on from inspiring English sources

If y is an absolutely function on [ t 0, T ] with range in R n such that d y ( t ) d t = f ( t, y ( t ), u ( t ) ), a.e.

The space of all q-absolutely functions on (A_{q,t}^) is denoted by (mathcal{A}C_{q}(A_{q,t}^)) and defined as the space of all q-regular at zero functions f satisfying sum_{j=0}^{infty}biglvert f bigl uq^{j}bigr -fbigl uq^{j+1}bigr bigrvert leq K quad mbigl uq^{j}bigr -fbigl uq^{j+1}bigr bigrvertant depending on the function f, cf. [33], Definition 4.3.1.

Let W be a non-negative, strictly increasing and locally absolutely continuous function on I. Suppose that (frac{dW x)}{dx}=w(x)), a.e.

A function is called a solution of the problem (1.11), (2.1) if it is a locally absolutely continuous function on, satisfies equation (1.11) on almost everywhere, and initial conditions (2.1) for.

If are absolutely continuous functions on, then is absolutely continuous on and the following equality is valid: (25).

where is the set of all absolutely continuous functions on.

Let be space of all absolutely continuous functions on.

Throughout the paper denotes the set of absolutely continuous functions on and is the norm in.

Also, AC [ 0, 1 ] is the set of absolutely continuous functions on [ 0, 1 ].

Suppose that and are absolutely continuous functions on such that for all,, (3.29).

In the following definition stands for the set of absolutely continuous functions on.