Sentence examples for the functional is from inspiring English sources

Let be two mappings satisfying the following conditions: (a) for each ; (b)for each fixed is a concave function; (c for each fixed, the functional is weakly lower semicontinuous function from to, that is, (2.21).

If the function is -strongly convex with constant and the functional is weakly upper semicontinuous on for each, then the auxiliary problem has a unique solution.

Since the function is strictly positive equality (3.10) implies that the functional is bounded from below.

The notation means that the functional is applied to considered as a function of.

In regarded of Assumption 2.9(c), for each fixed we have that the functional is an upper semicontinuous functional; this together with the weak continuity of the function, we obtain (4.21).

The functional is said to be nonnegative over the class of admissible functions if J ( x ) ≥ 0 for every admissible x.

Then the functional is continuous.

where and Moreover, the functional is.

[H7.1] The functional is Borel measurable.

The functional is continuous and is continuous.

[H7.5] The functional is continuous and nonnegative.