Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

TIME SCALES INTEGRAL INEQUALITIES FOR SUPERQUADRATIC FUNCTIONS

  • Baric, Josipa (Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture University of Split) ;
  • Bibi, Rabia (Centre for Advanced Mathematics and Physics National University of Sciences and Technology) ;
  • Bohner, Martin (Department of Mathematics and Statistics Missouri University of Science and Technology) ;
  • Pecaric, Josip (Faculty of Textile Technology University of Zagreb)
  • Received : 2011.11.24
  • Published : 2013.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals.

Keywords

References

  1. S. Abramovich, S. Banic, M. Matic, and J. Pecaric, Jensen-Steffensen's and related inequalities for superquadratic functions, Math. Inequal. Appl. 11 (2008), no. 1, 23-41.
  2. S. Abramovich, J. Baric, and J. Pecaric, A variant of Jessen's inequality of Mercer's type for superquadratic functions, J. Inequal. Pure Appl. Math. 9 (2008), no. 3, Article 62, 13 pages.
  3. S. Abramovich, G. Jameson, and G. Sinnamon, Inequalities for averages of convex and superquadratic functions, J. Inequal. Pure Appl. Math. 5 (2004), no. 4, Article 91, 14 pp.
  4. S. Abramovich, Refining Jensen's inequality, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47(95) (2004), no. 1-2, 3-14.
  5. R. P. Agarwal, M. Bohner, and A. Peterson, Inequalities on time scales: a survey, Math. Inequal. Appl. 4 (2001), no. 4, 535-557.
  6. 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, 16 pp.
  7. S. Banic, J. Pecaric, and, S. Varosanec, Superquadratic functions and refinements of some classical inequalities, J. Korean Math. Soc. 45 (2008), no. 2, 513-525. https://doi.org/10.4134/JKMS.2008.45.2.513
  8. S. Banic and S. Varosanec, Functional inequalities for superquadratic functions, Int. J. Pure Appl. Math. 43 (2008), no. 4, 537-549.
  9. J. Baric, Superquadratic functions, PhD thesis, University of Zagreb, Zagreb, Croatia, 2007.
  10. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhauser Boston Inc., Boston, MA, 2001.
  11. C. Dinu, Hermite-Hadamard inequality on time scales, J. Inequal. Appl. 2008 (2008), Art. ID 287947, 24 pp.
  12. S. Hilger, Ein MaBkettenkalkul mit Anwendung auf Zentrumsmannigfaltigkeiten, PhD thesis, Universitat Wurzburg, 1988.
  13. S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18 (1990), no. 1-2, 18-56. https://doi.org/10.1007/BF03323153
  14. S. Hilger, Differential and difference calculus-unified!, Proceedings of the Second World Congress of Nonlinear Analysts, Part 5 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 5, 2683-2694.
  15. J. L. W. V. Jensen, Sur les fonctions convexes et les inegalites entre les valeurs moyennes, Acta Math. 30 (1906), no. 1, 175-193. https://doi.org/10.1007/BF02418571
  16. J. Pecaric, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, volume 187 of Mathematics in Science and Engineering, Academic Press Inc., Boston, MA, 1992.

Cited by

  1. Time scale Hardy-type inequalities with ‘broken’ exponent p vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-014-0533-z
  2. ON REFINEMENTS OF HÖLDER'S INEQUALITY II vol.32, pp.1, 2016, https://doi.org/10.7858/eamj.2016.003