Some Improvements on Hilbert's Integral Inequality

A Further Generalization of Hardy-Hilbert's Integral Inequality with Parameter and Applications

“…When p = q = 2, the inequality (3.9) reduces, after some simple computation, to an inequality obtained in [2].…”

“…After simple computation, the inequality (4.4) is equivalent to the inequality (3.4) in [2]. Consequently, inequality (4.2) is an extension of (3.4) in [2].…”

“…The main purpose of this paper is to establish a new extended Hardy-Hilbert's type inequality, which includes improvements and generalisations of the corresponding results from [2]- [3].…”

On the Hubert Inequality

“…The proofs of Lemmas 1 and 2 have been given in our previous paper [1]. Lemma 3 is actually a sharpening of the Cauchy-Schwarz inequality.…”

“…is called the Hubert integral inequality. The constant ir contained in these inequalities, especially in (1), was proved to be the best possible (see [ 3]) . However, if 0 < E 00 a < : or 0 < b 2 < oo, then we can select a number r > 0 such that the right-hand side of (1) can be replaced by i.e.…”