Generalizations of Minkowski and Beckenbach-Dresher Inequalities and Functionals on Time Scales

Main Article Content

Rabia Bibi
Anees Ur Rahman
Muhammad Shahzad

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.

Article Details

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.