International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 4, Pages 237-250
doi:10.1155/S0161171201005816
On Bicheng[Yang]-Debnath's generalizations of Hardy's integral inequality
Aleksandra Čižmešija1
and Josip Pečarić2
1Department of Mathematics, University of Zagreb, Bijeni {c}ka cesta 30, Zagreb 10000, Croatia
2Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia
Abstract
We consider Hardy's integral inequality and we obtain some new generalizations of Bicheng-Debnath's recent results. We derive two distinguished classes of inequalities covering all admissible choices of parameter k from Hardy's original relation. Moreover, we prove the constant factors involved in the right-hand sides of some particular inequalities from both classes to be the best possible, that is, none of them can be replaced with a smaller constant.