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BOUNDS FOR HARDY DIFFERENCES

Part of: Inequalities

Published online by Cambridge University Press:  08 August 2011

SABIR HUSSAIN  and
JOSIP PEČARIĆ
SABIR HUSSAIN*
Affiliation:
Institute of Space Technology, Near Rawat Tool Plaza, Islamabad Highway, Islamabad, Pakistan (email: sabirhus@gmail.com)
JOSIP PEČARIĆ
Affiliation:
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan University of Zagreb, Faculty of Textile Technology, 10000 Zagreb, Croatia (email: pecaric@mahazu.hazu.hr)
*
✉For correspondence; e-mail: sabirhus@gmail.com
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Abstract

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Bounds for Hardy differences, that is, improvements and reverses of the well-known Hardy inequality, are obtained.

Keywords

logarithmic convexityBoas inequalityHardy inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 2 , October 2010 , pp. 218 - 224
Copyright
Copyright © Australian Mathematical Society 2011

References

[1]Bicheng, Y., Zhuohua, Z. and Debnath, L., “On new generalizations of Hardy’s integral inequality”, J. Math. Anal. Appl. 217 (1998) 321–327, doi:10.1006/jmaa.1998.5758.CrossRefGoogle Scholar
[2]Boas, R. P., “Some integral inequalities related to Hardy’s inequality”, J. Anal. Math. 23 (1970) 53–63, doi:10.1007/BF02795488.CrossRefGoogle Scholar
[3]Hardy, G. H., “Note on a theorem of Hilbert”, Math. Z. 6 (1920) 314–317, doi:10.1007/BF01199965.CrossRefGoogle Scholar
[4]Hardy, G. H., “Notes on some points in the integral calculus, LX: an inequality between integrals (60)”, Messenger Math. 54 (1925) 150–156.Google Scholar
[5]Imoru, C. O., “On some extensions of Hardy’s inequality”, Int. J. Math. Math. Sci. 8 (1995) 165–171, doi:10.1155/S0161171285000151.CrossRefGoogle Scholar
[6]Izumi, M., Izumi, S. and Peterson, G., “On Hardy’s inequality and its generalization”, Tohoku Math. J. 21 (1999) 601–613, doi:10.2748/tmj/1178242904.Google Scholar
[7]Pečarić, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings, and statistical applications (Academic Press, San Diego, CA, 1992).Google Scholar
[8]Simic, S., “On logarithmic convexity for differences of power means”, J. Inequal. Appl. 2007 (2007) Article ID 37359, 8 pages, doi:10.1155/2007/37359.CrossRefGoogle Scholar