Sentence examples for functional on is from inspiring English sources

The functional on is given by (1.6).

When contains constants, a linear functional on is called a mean on if.

A continuous linear functional on is said to be an invariant mean or a -mean if and only if.

A linear functional on is said to be a Banach limit (see [5]) if it has the following properties: (1) if for all ; (2) where ; (3), where the shift operator is defined by.

A map is said to be a nonnegative continuous concave functional on if is a continuous and (1.3).

A map is said to be a nonnegative continuous concave functional on if is continuous and (5.1).

The map is a nonnegative continuous concave functional on provided is continuous and (21).

Similarly, the map is a nonnegative continuous convex functional on provided is continuous and (22).

For f ( t ) ∈ F, the linear functional on ℙ is defined by 〈 f ( t ) | x n 〉 = a n.

Let and be nonnegative continuous convex functionals on a cone, be a nonnegative continuous concave functional on, and be a nonnegative continuous functional on satisfying for, such that for some positive numbers and (25).

Let be nonnegative, continuous, convex functionals on and be a nonnegative, continuous, concave functionals on, and be a nonnegative continuous functionals on.