| 1. |
- Kufner, Alois, et al.
(författare)
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Generalized weighted inequality with negative powers
- 2007
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Ingår i: Journal of Mathematical Inequalities. - : Element d.o.o.. - 1846-579X .- 1848-9575. ; 1:2, s. 269-280
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Tidskriftsartikel (refereegranskat)abstract
- In this paper necessary and sufficient conditions for the validity of the generalized Hardy inequality for the case -∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore, some special cases are considered
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| 2. |
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| 3. |
- Oguntuase, James, et al.
(författare)
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Weighted multidimensional Hardy type inequalities via Jensen's inequality
- 2007
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Ingår i: Proceedings of A. Razmadze Mathematical Institute. - 1512-0007. ; 144, s. 91-105
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Tidskriftsartikel (refereegranskat)abstract
- The authors prove that Jenson's inequality implies some sharp weighted multidimensional Hardy type inequalities. In particular, their results unify and further extend several results of this type in the literature including the recent results in [A. Čižmešija, J. E. Pečarić and L. E. Persson, J. Approx. Theory 125 (2003), no. 1, 74--84; MR2016841 (2004i:42017); S. Kaijser et al., Math. Inequal. Appl. 8 (2005), no. 3, 403--417; MR2148234 (2006c:26036); S. Kaijser, L. E. Persson and A. Öberg, J. Approx. Theory 117 (2002), no. 1, 140--151; MR1920123 (2003f:26037)]. The main result is obtained in Theorem 3.1. In Section 4, the authors show that some existing results are special cases of the theorems obtained in this paper.
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| 4. |
- Adeleke, E.O., et al.
(författare)
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On a new class of Hardy-type inequalities
- 2012
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2012:259
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.
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| 5. |
- Oguntuase, James Adedayo, et al.
(författare)
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Refinements of Hardy-type inequalities via superquadracity
- 2016
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Ingår i: Publicationes mathematicae (Debrecen). - 0033-3883 .- 2064-2849. ; 88:3-4, s. 467-476
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Tidskriftsartikel (refereegranskat)abstract
- Some new refinements of Hardy-type integral inequalities are derived, proved and discussed using the concept of superquadratic and subquadratic functions. The results obtained are generalizations and improvements of inequalities of this type in the literature.
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| 6. |
- Oguntuase, James, et al.
(författare)
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Hardy type inequalities via convexity : the jouney so far
- 2010
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Ingår i: The Australian Journal of Mathematical Analysis and Applications. - 1449-5910. ; 7:2
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Tidskriftsartikel (refereegranskat)abstract
- It is nowadays well-known that Hardy's inequality (like many other inequalities) follows directly from Jensen's inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.
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| 7. |
- Oguntuase, James, et al.
(författare)
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Mulitdimensional Hardy type inequalities for p
- 2007
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Ingår i: Journal of Mathematical Inequalities. - : Element d.o.o.. - 1846-579X .- 1848-9575. ; 1:1, s. 1-11
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Tidskriftsartikel (refereegranskat)
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| 8. |
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| 9. |
- Oguntuase, James, et al.
(författare)
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Multidimensional Hardy-type inequalities via convexity
- 2008
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Ingår i: Bulletin of the Australian Mathematical Society. - 0004-9727 .- 1755-1633. ; 77:2, s. 245-260
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Tidskriftsartikel (refereegranskat)abstract
- Let an almost everywhere positive function Φ be convex for p>1 and p<0, concave for p∈(0,1), and such that Axp≤Φ(x) ≤Bxp holds on ℝ+ for some positive constants A≤B. In this paper we derive a class of general integral multidimensional Hardy-type inequalities with power weights, whose left-hand sides involve Φ (∫0x1⋯∫0xnf(t) dt) instead of [(∫0x1⋯∫0xnf(t) dt]p, while the corresponding right-hand sides remain as in the classical Hardy's inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature.
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| 10. |
- Oguntuase, James, et al.
(författare)
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Multidimensional Hardy-type inequalities with general kernels
- 2008
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 348:1, s. 411-418
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Tidskriftsartikel (refereegranskat)abstract
- Some new multidimensional Hardy-type inequalities involving arithmetic mean operators with general positive kernels are derived. Our approach is mainly to use a convexity argument and the results obtained improve some known results in the literature and, in particular, some recent results in [S. Kaijser, L. Nikolova, L.-E. Persson, A. Wedestig, Hardy-type inequalities via convexity, Math. Inequal. Appl. 8 (3) (2005) 403-417] are generalized and complemented.
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