Sentence examples for inequality establish from inspiring English sources

All of these observations, combined with the fact that the equation evolves only in a number of steps equal to the dimension of its state space, combined with the discrete Gronwall inequality, establish that the difference equation has bounded solutions.

This paper extends a stability estimate of the Sobolev Inequality established by Bianchi and Egnell in [3].

The new inequality established is significant in theory and applications.

This is just an inequality established by Das [28].

This is just an inequality established by Beesack [30].

Then above inequality becomes the following inequality: This is just an inequality established by Yang [32].

Using the inequalities in the last two displays together with (180) and triangle inequality establishes (170).

The inequality established in Theorem 2.2 generalizes that reported in [7, Theorem 3.2].

Obviously, for n ≥ 2, (2.4) is sharper than the following inequality established by Willett [29].

Then (2.8) becomes the following inequality: This is just an inequality established by Agarwal and Thandapani [31].

In that paper he proved the manifold counterpart of the classical isoperimetric inequality established by De Giorgi in [53].