EN
A generalization of reverse Hölder's inequality via the diamond-$\alpha$ integral on time scales
Abstract
In this paper, we give a generalization of the reverse H\"{o}lder's diamond-$\alpha$ inequality on time scales by introducing two parameters. We note that many inequalities related to the H\"{o}lder's inequality can be obtained via this inequality.
Keywords
References
- [1] B. Benaissa and H. Budak, More on reverse of Hölder’s integral inequality, Korean. J. Math. 28, 9–15, 2020.
- [2] R.P. Agarwal, D. O’Regan, and S.H. Saker, Hardy Type Inequalities on Time Scales, Springer International Publishing, Switzerland, 2016.
- [3] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
- [4] G. Chen and Z. Chen, A functional generalization of the reverse Hölder integral inequality on time scales, Math. Comput. Model. 54, 2939–2942, 2011.
- [5] U.M. Özkan, M.Z. Sarikaya and H. Yildirim, Extensions of certain integral inequali- ties on time scales, Appl. Math. Lett. 21 (10), 993–1000, 2008.
- [6] D. O’Regan, H.M. Rezk, and S.H. Saker, Some dynamic inequalities involving Hilbert and Hardy-Hilbert operators with kernels, Results Math. 73 (4), 146, 2018.
- [7] J.W. Rogers, Q. Sheng, Notes on the diamond-alpha dynamic derivative on time scales, J. Math. Anal. Appl. 326 (1), 228–241, 2007.
- [8] M.Z. Sarikaya, H. Yildirim, and U.M. Özkan, Time scale integral inequalities similar to Qi’s inequality, J. Ineq. Pur. Appl. Math. 7 (4), 128, 2006.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Publication Date
April 1, 2022
Submission Date
March 10, 2021
Acceptance Date
September 29, 2021
Published in Issue
Year 2022 Volume: 51 Number: 2
APA
Benaissa, B. (2022). A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales. Hacettepe Journal of Mathematics and Statistics, 51(2), 383-389. https://doi.org/10.15672/hujms.877967
AMA
1.Benaissa B. A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales. Hacettepe Journal of Mathematics and Statistics. 2022;51(2):383-389. doi:10.15672/hujms.877967
Chicago
Benaissa, Bouharket. 2022. “A Generalization of Reverse Hölder’s Inequality via the Diamond-$\alpha$ Integral on Time Scales”. Hacettepe Journal of Mathematics and Statistics 51 (2): 383-89. https://doi.org/10.15672/hujms.877967.
EndNote
Benaissa B (April 1, 2022) A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales. Hacettepe Journal of Mathematics and Statistics 51 2 383–389.
IEEE
[1]B. Benaissa, “A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, pp. 383–389, Apr. 2022, doi: 10.15672/hujms.877967.
ISNAD
Benaissa, Bouharket. “A Generalization of Reverse Hölder’s Inequality via the Diamond-$\alpha$ Integral on Time Scales”. Hacettepe Journal of Mathematics and Statistics 51/2 (April 1, 2022): 383-389. https://doi.org/10.15672/hujms.877967.
JAMA
1.Benaissa B. A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales. Hacettepe Journal of Mathematics and Statistics. 2022;51:383–389.
MLA
Benaissa, Bouharket. “A Generalization of Reverse Hölder’s Inequality via the Diamond-$\alpha$ Integral on Time Scales”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, Apr. 2022, pp. 383-9, doi:10.15672/hujms.877967.
Vancouver
1.Bouharket Benaissa. A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales. Hacettepe Journal of Mathematics and Statistics. 2022 Apr. 1;51(2):383-9. doi:10.15672/hujms.877967
Cited By
New Diamond-α Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
Axioms
https://doi.org/10.3390/axioms11070323