On Hilbert-Type and Hardy-Type Integral Inequalities and Applications by Bicheng Yang & Michael Th. Rassias

Author:Bicheng Yang & Michael Th. Rassias
Language: eng
Format: epub
ISBN: 9783030292683
Publisher: Springer International Publishing

(3.11)

Since for we have

and

by (3.11) and the Lebesgue dominated convergence theorem (cf. [2]), we have

This completes the proof of the lemma.

3.2 Main Results

Theorem 3.3

Suppose that M is a positive constant. The following statements (i), (ii), (iii) and (iv) are equivalent:

(i) For any satisfying

we have the following inequality:

(3.12)

(ii) For any satisfying

we have the following inequality:

(3.13)

(iii) For any satisfying

and satisfying

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.