Sentence examples for by the function defined from inspiring English sources

Denote by the function defined as (2.24).

Throughout this paper, we denote by the function defined by.

Denote by the function defined on by the formula (213).

For each with, we denote by the function defined by (3.6).

Throughout this paper, we denote by the function defined by (22).

Since the proof of Lemma 2.5 shows that, and hence by, the function defined by (3.34).

If we suppose that and obey merely (3.1) and (3.2), and that (where is the space defined by (3.4)), the function defined in (3.3a), (3.3b), and (3.3c) is well defined and continuous on.

For (x cdot) in C([sigma, a], [D])), we denote by (q(s)) the function defined by (3.10).

The function defined by (1.6) was introduced and studied by Srivastava and Panda [37].

The function defined by.

The function defined by (3.1).