Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus

Muhammad Jibril Shahab Sahir

Communications in Mathematics (2020)

  • Volume: 28, Issue: 3, page 277-287
  • ISSN: 1804-1388

Abstract

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The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon's Inequality, Bergström's Inequality, Schlömilch's Inequality and Rogers-Hölder's Inequality on time scales in comprehensive form.

How to cite

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Sahir, Muhammad Jibril Shahab. "Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus." Communications in Mathematics 28.3 (2020): 277-287. <http://eudml.org/doc/296994>.

@article{Sahir2020,
abstract = {The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon's Inequality, Bergström's Inequality, Schlömilch's Inequality and Rogers-Hölder's Inequality on time scales in comprehensive form.},
author = {Sahir, Muhammad Jibril Shahab},
journal = {Communications in Mathematics},
keywords = {Time scales; Radon's Inequality; Bergström's Inequality; Schlömilch's Inequality; Rogers-Hölder's Inequality},
language = {eng},
number = {3},
pages = {277-287},
publisher = {University of Ostrava},
title = {Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus},
url = {http://eudml.org/doc/296994},
volume = {28},
year = {2020},
}

TY - JOUR
AU - Sahir, Muhammad Jibril Shahab
TI - Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 3
SP - 277
EP - 287
AB - The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon's Inequality, Bergström's Inequality, Schlömilch's Inequality and Rogers-Hölder's Inequality on time scales in comprehensive form.
LA - eng
KW - Time scales; Radon's Inequality; Bergström's Inequality; Schlömilch's Inequality; Rogers-Hölder's Inequality
UR - http://eudml.org/doc/296994
ER -

References

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  1. Agarwal, R.P., O'Regan, D., Saker, S.H., Dynamic Inequalities on Time Scales, 2014, Springer International Publishing, Cham, Switzerland, (2014) MR3307947
  2. Ammi, M.R.S., Torres, D.F.M., Hölder's and Hardy's two dimensional diamond-alpha inequalities on time scales, Ann. Univ. Craiova, Math. Comp. Sci. Series, 37, 1, 2010, 1-11, (2010) MR2609350
  3. Anderson, D., Bullock, J., Erbe, L., Peterson, A., Tran, H., Nabla dynamic equations on time scales, Panam. Math. J., 13, 1, 2003, 1-48, (2003) MR1953216
  4. Beckenbach, E.F., Bellman, R., Inequalities, 1961, Springer, Berlin, Göttingen and Heidelberg, (1961) MR0158038
  5. Bellman, R., 10.2307/2306621, Amer. Math. Monthly, 62, 3, 1955, 172-173, (1955) MR0072834DOI10.2307/2306621
  6. Bergström, H., A triangle inequality for matrices, In Den Elfte Skandinaviske Matematikerkongress (1949) Trondheim, Johan Grundt Tanums Forlag, Oslo, 1952, 264-267, (1952) MR0053064
  7. Bohner, M., Peterson, A., Dynamic Equations on Time Scales, 2001, Birkhäuser Boston, Inc., Boston, MA, (2001) Zbl0993.39010MR1843232
  8. Bohner, M., Peterson, A., Advances in Dynamic Equations on Time Scales, 2003, Birkhäuser Boston, Boston, MA, (2003) Zbl1025.34001MR1843232
  9. Bătineţu-Giurgiu, D.M., Pop, O.T., A generalization of Radon's inequality, Creative Math. & Inf., 19, 2, 2010, 116-121, (2010) MR2761455
  10. Bătineţu-Giurgiu, D.M., Stanciu, N., New generalizations and new approaches for two IMO problems, Journal of Science and Arts, 12, 1, 2012, 25-34, (2012) MR2911825
  11. Bătineţu-Giurgiu, D.M., Mărghidanu, D., Pop, O.T., 10.37193/CMI.2018.02.03, Creat. Math. Inform., 27, 2, 2018, 115-122, (2018) MR3885356DOI10.37193/CMI.2018.02.03
  12. Hardy, G.H., Littlewood, J.E., Pölya, G., Inequalities, 1952, 2nd Ed., Cambridge, University Press, (1952) MR0046395
  13. Hilger, S., Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, 1988, Ph.D. Thesis, Universität Würzburg, (1988) Zbl0695.34001
  14. Hölder, O., Über einen Mittelwertsatz, Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der GeorgAugusts-Universität zu Göttingen, 1889, 38-47, (1889) 
  15. Mitrinović , D.S., Analytic Inequalities, 1970, Springer-Verlag, Berlin, (1970) MR0274686
  16. Radon, J., Theorie und Anwendungen der absolut additiven Mengenfunktionen, Sitzungsber. Acad. Wissen. Wien, 122, 1913, 1295-1438, (1913) 
  17. Sahir, M.J.S., Hybridization of classical inequalities with equivalent dynamic inequalities on time scale calculus, The Teaching of Mathematics, XXI, 1, 2018, 38-52, (2018) MR3782912
  18. Sahir, M.J.S., 10.15826/umj.2018.2.010, Ural Math. J., 4, 2, 2018, 88-98, (2018) MR3901588DOI10.15826/umj.2018.2.010
  19. Sheng, Q., Fadag, M., Henderson, J., Davis, J.M., 10.1016/j.nonrwa.2005.03.008, Nonlinear Analysis: Real World Appl., 7, 3, 2006, 395-413, (2006) MR2235865DOI10.1016/j.nonrwa.2005.03.008

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