Sentence examples for by using the way from inspiring English sources

In recent years, by using the way of weight functions, a number of extensions of (1) were given by Yang (cf. [3]).

By using the way of weight functions and the technique of real analysis, a half-discrete Hardy-Hilbert's inequality with two interval variables is derived.

In this paper, by using the way of weight coefficient and the theory of operators, we define a new Hilbert-type operator and obtain its norm.

By using the way of weight functions and the Hermite-Hadamard inequality, a half-discrete reverse Mulholland-type inequality with a best constant factor is given.

By using the way of weight functions and Jensen-Hadamard's inequality, a more accurate half-discrete Mulholland's inequality with a best constant factor is given.

By using the way of weight functions and Hadamard's inequality, a half-discrete Hilbert-type inequality similar to Mulholland's inequality with a best constant factor is given.

By using the same way as in Corollary 4.10, we can get Corollary 4.11.

By virtue of Lemma 4, we can obtain the following results by using the similar way as to those of Theorem 8.

The significance of the differences of mean frequency of headache between faculty grades were compared by using the one way ANOVA test.

By using the same way as in the proof Theorem 3.1, we may construct a f-g-sequence ({fx_{n}}) of initial point (x_{0}).

Comparison of two groups (means) was performed by using the one-way ANOVA and Student's t test for the comparison of paired samples.