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Year 2022, Volume: 51 Issue: 2, 383 - 389, 01.04.2022
https://doi.org/10.15672/hujms.877967

Abstract

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.
  • [9] L. Yin and F. Qi, Some integral inequalities on time scales, Results Math. 64, 371– 381, 2013.
  • [10] M. Zakarya, H.A. Abdelhamid, G. Alnemer and H.M. Rezk More on Hölder’s in- equality and it’s reverse via the diamond-alpha integral, Symmetry, 12 (10), 1716, 2020.

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

Year 2022, Volume: 51 Issue: 2, 383 - 389, 01.04.2022
https://doi.org/10.15672/hujms.877967

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.

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.
  • [9] L. Yin and F. Qi, Some integral inequalities on time scales, Results Math. 64, 371– 381, 2013.
  • [10] M. Zakarya, H.A. Abdelhamid, G. Alnemer and H.M. Rezk More on Hölder’s in- equality and it’s reverse via the diamond-alpha integral, Symmetry, 12 (10), 1716, 2020.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Bouharket Benaissa 0000-0002-1195-6169

Publication Date April 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 2

Cite

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 Benaissa B. A generalization of reverse Hölder’s inequality via the diamond-$\alpha$ integral on time scales. Hacettepe Journal of Mathematics and Statistics. April 2022;51(2):383-389. doi:10.15672/hujms.877967
Chicago Benaissa, Bouharket. “A Generalization of Reverse Hölder’s Inequality via the Diamond-$\alpha$ Integral on Time Scales”. Hacettepe Journal of Mathematics and Statistics 51, no. 2 (April 2022): 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 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, 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 2022), 383-389. https://doi.org/10.15672/hujms.877967.
JAMA 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, 2022, pp. 383-9, doi:10.15672/hujms.877967.
Vancouver 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):383-9.