Sentence examples for modulus of smoothness from inspiring English sources

We present, by making use of multivariate approximation tools, a quantitative upper bound estimation on approximation accuracy of the simultaneous approximation of the FNNs in terms of the modulus of smoothness of the functions to be approximated.

(Modulus of smoothness [1 3]).

Let be the modulus of smoothness of defined by (2.6).

where is the modulus of smoothness of, defined by.

The following lemma is easily proved by the definition of modulus of smoothness: Lemma 3.1.

First, we define the Ditzian Totik modulus of smoothness and the Peetre K-functional.

We define a function, called the modulus of smoothness of, as follows: (1.3).

We then can define the modulus of smoothness of, as (26).

They also obtained some direct estimations for error with the help of weighted modulus of smoothness.

The modulus of smoothness of a Banach space is the function defined by (2.1).

The modulus of smoothness of is the function defined by (2.2).