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SOME REVERSE DYNAMIC INEQUALITIES ON TIME SCALES

Part of: Real functions: Miscellaneous topics Inequalities

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. 

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