Research Article
Generalizations of Minkowski and Beckenbach-Dresher Inequalities and Functionals on Time Scales
- Abbottabad University of Science and Technology
- Hazara University
* Corresponding author
Abstract
We generalize integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality.
How to Cite
R. Bibi, A. U. Rahman, M. Shahzad, Generalizations of Minkowski and Beckenbach-Dresher Inequalities and Functionals on Time Scales, Int. J. Anal. Appl. 18 (2020), 319–331. https://doi.org/10.28924/2291-8639-18-2020-319
BibTeX
@article{Bibi2020,
author = {Bibi, Rabia and Rahman, Anees Ur and Shahzad, Muhammad},
title = {Generalizations of Minkowski and Beckenbach-Dresher Inequalities and Functionals on Time Scales},
journal = {Int. J. Anal. Appl.},
volume = {18},
year = {2020},
pages = {319--331},
doi = {10.28924/2291-8639-18-2020-319}
}References
- [1] M. Anwar, R. Bibi, M. Bohner, and J. Pecaric, Integral inequalities on time scales via the theory of isotonic linear functionals, Abstr. Appl. Anal. 2011(2011), Art. ID 483595.
- [2] R. Bibi, M. Bohner, J. Pecaric, and S. Varosanec, Minkowski and Beckenbach-Dresher inequalities and functionals on time scales, J. Math. Inequal. Appl. 2013(2013), 299-312.
- [3] M. Bohner and A. Peterson, Dynamic equations on time scales: An introduction with applications, Birkh ¨auser, Boston, 2001.
- [4] M. Bohner and G. Sh. Guseinov, Multiple integration on time scales, Dynam. Systems Appl. 14 (2005), 579-606.
- [5] M. Bohner and G. Sh. Guseinov, Multiple Lebesgue integration on time scales, Adv. Difference Equ. 2006 (2006), Art. ID 26391.
- [6] B. Guljas, C. E. M. Pearce, and J. Pecaric, Some generalizations of the Beckenbach-Dresher inequality, Houston J. Math. 22 (1996), 629-638.
- [7] S. Hilger, Ein Maßkettenkalkul mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph. D. thesis, Universit ¨at W ¨urzburg, 1988.
- [8] S. Hilger, Analysis on measure chains ”” a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.
- [9] B. Ivankovic, J. Pecaric, and S. Varosanec, Properties of mappings related to the Minkowski inequality, Mediterranean J. Math. 8 (2011), 543-551.
- [10] S. Varosanec, A generalized Beckenbach-Dresher inequality and related results, Banach J. Math. Anal. 4 (2010), 13-20.