Research Article

A generalization of reverse Hölder's inequality via the diamond-$\alpha$ integral on time scales

Volume: 51 Number: 2 April 1, 2022
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

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  2. [2] R.P. Agarwal, D. O’Regan, and S.H. Saker, Hardy Type Inequalities on Time Scales, Springer International Publishing, Switzerland, 2016.
  3. [3] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
  4. [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. [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. [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. [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. [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

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

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