Abstract
Laith Emil Azar Department of Mathematics, Al Al-Bayt University, P.O. Box. 130095, Mafraq 25113, Jordan Correspondence should be addressed to Laith Emil Azar, azar laith@yahoo.com Received 23 October 2007; Accepted 2 January 2008 Recommended by Shusen Ding By introducing some parameters we establish an extension of Hardy-Hilbert’s integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered. Copyright q 2008 Laith Emil Azar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Highlights
Journal of Inequalities and Applications where the constant factors π/ sin π/p and pq are the best possible in 1.3 and 1.4 , respectively
If f x,g x ≥ 0, 0 < ∞ 0 f x dx < ∞, and ∞ 0 g2 x dx ∞, see∞f xg y 0 x y dx dy < π ∞f2 x dx g2 x dx
Setting t x/y λ, we find xλ/2−1−ε/p y λ/2−1−ε/q
Summary
Journal of Inequalities and Applications where the constant factors π/ sin π/p and pq are the best possible in 1.3 and 1.4 , respectively. N1 where the constant factor D A, B see 7, Lemma 2.1 is the best possible in both inequalities.
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