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SOME REVERSE DYNAMIC INEQUALITIES ON TIME SCALES

Part of: Inequalities Real functions: Miscellaneous topics

Published online by Cambridge University Press:  17 August 2017

R. P. AGARWAL ,
R. R. MAHMOUD ,
D. O’REGAN  and
S. H. SAKER
R. P. AGARWAL*
Affiliation:
Department of Mathematics, Texas A&M University–Kingsville, Texas 78363, USA email agarwal@tamuk.edu
R. R. MAHMOUD
Affiliation:
Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt email rrm00@fayoum.edu.eg
D. O’REGAN
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland email donal.oregan@nuigalway.ie
S. H. SAKER
Affiliation:
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt email shsaker@mans.edu.eg
*
✉agarwal@tamuk.edu
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Abstract

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In this paper, we prove some new reverse dynamic inequalities of Renaud- and Bennett-type on time scales. The results are established using the time scales Fubini theorem, the reverse Hölder inequality and a time scales chain rule.

Keywords

Bennett’s inequalityreverse inequalitiestime scales

MSC classification

Primary: 26E70: Real analysis on time scales or measure chains
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 445 - 454
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Bennett, G., ‘Lower bounds for matrices’, Linear Algebra Appl. 82 (1986), 81–98.CrossRefGoogle Scholar
Bibi, R., Bohner, M., Pečarić, J. and Varosanec, S., ‘Minkowski and Beckenbach–Dresher inequalities and functionals on time scales’, J. Math. Inequal. 3 (2013), 299–312.Google Scholar
Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Birkhäuser, Boston, MA, 2001).Google Scholar
Copson, E. T., ‘Note on series of positive terms’, J. Lond. Math. Soc. 2 (1927), 9–12.CrossRefGoogle Scholar
Hardy, G. H., ‘Notes on a theorem of Hilbert’, Math. Z. 6 (1920), 314–317.CrossRefGoogle Scholar
Hardy, G. H., ‘Notes on some points in the integral calculus (LX). An inequality between integrals’, Messenger Math. 54 (1925), 150–156.Google Scholar
Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities, 2nd edn (Cambridge University Press, Cambridge, 1952).Google Scholar
Lyons, R., ‘A lower bound on the Cesàro operator’, Proc. Amer. Math. Soc. 86(4) (1982), 694.Google Scholar
Milman, M., ‘A note on reversed Hardy inequalities and Gehring’s lemma’, Commun. Pure Appl. Math. 50(4) (1997), 311–315.Google Scholar
Řehák, P., ‘Hardy inequality on time scales and its application to half-linear dynamic equations’, J. Inequal. Appl. 5 (2005), 495–507.Google Scholar
Renaud, P. F., ‘A reversed Hardy inequality’, Bull. Aust. Math. Soc. 34(2) (1986), 225–232.Google Scholar
Tuna, A. and Kutukcu, S., ‘Some integral inequalities on time scales’, Appl. Math. Mech. 29(1) (2008), 23–29 (English Ed.).Google Scholar
Xiao, J., ‘A reverse BMO-Hardy inequality’, Real Anal. Exchange 25(2) (1999), 673–678.Google Scholar