10.71932/ijm.2024.1198100

Improvements of Some Inequalities via Steffensen-Popoviciu Measure and it’s Dual

  1. Department of Mathematics, Faculty of Science, Lorestan University, 6815144316, Khoramabad, Iran.

Received: 30-10-2024

Accepted: 25-12-2024

Published in Issue 30-12-2024

How to Cite

Nazari Pasari, S., Abbasi, N., & Barani, A. (2024). Improvements of Some Inequalities via Steffensen-Popoviciu Measure and it’s Dual. International Journal of Mathematical Modelling & Computations, 14(4), 335-344. https://doi.org/10.71932/ijm.2024.1198100

Abstract

In this paper we establish new inequalities for convex and strongly convex defined on intervals in framework of Steffensen-Popoviciu and Dual Steffensen-Popoviciu measures are introduced. Some inequalities in this setting are also involved. Suitable examples are also involved are given.

Keywords

  • Dual Steffensen-Popoviciu measure,
  • Convex function,
  • Strongly convex function,
  • Coordinated concave.

References

  1. S.S. Dragomir, On the Hadamard’s inequlality for convex functions on the coordinates in a rectangle
  2. from the plane, Taiwanese journal of mathematics, 2001 Dec 1:775-88.
  3. A.M. Fink, A best possible Hadamard inequality, Math. Inequal. Appl, 1998;1(2):223-30.
  4. J.B. Hiriart-Urruty, C. Lemarchal,Fundamentals of convex analysis, Springer Science & Business
  5. Media, 2004.
  6. S. Nazari Pasari, A. Barani, N. Abbasi, Generalized integral Jensen inequality, Journal of Inequalities
  7. and Applications, 2024 Feb 20;2024(1):25.
  8. C. P. Niculescu, On a result of G. Bennett, Bulletin mathmatique de la Socit des Sciences Mathmatiques de Roumanie, 2011 Jan 1:261-7.
  9. C. P. Niculescu, L. E. Persson, Convex functions and their applications, Vol. 23. New York: Springer,
  10. C. P. Niculescu, C. I. Spiridon, New Jensen-type inequalities, Journal of Mathematical Analysis and
  11. Applications, 401(1), 343-348.
  12. C. P. Niculescu, M. M. Stanescu, The SteffensenPopoviciu measures in the context of quasiconvex
  13. functions, J. Math. Inequal, 2017 Jun 1;11:469-83.
  14. J. Pecaric, F. Proschan, Y. L. Tong,Convex functions, partial orderings, and statistical applications,
  15. Academic Press, Boston, 1982.
  16. B. T. Polyak,Existence theorems and convergence of minimizing sequences in extremum problems
  17. with restrictions, Soviet Math. Dokl. 7, 7275, 1966
  18. T. Popoviciu, Notes sur les fonctions convexes d’ordre suprieur (IX), Bulletin Mathmatique de la
  19. socit Roumaine des Sciences, 1941 Jan 1;43(1/2):85-141.
  20. A. W. Roberts, D. E. Varberg,Convex Functions, Academic Press, New York (1973)
  21. H. M. Srivastava, S. Mehrez, S. M. Sitnik, Hermite-Hadamard-type integral inequalities for convex
  22. functions and their applications, Mathematics, 2022 Aug 31;10(17):3127.