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Weighted Steffensen Type Inequalities Involving Convex Functions

Year 2018, Volume: 6 Issue: 1, 84 - 91, 15.04.2018

Abstract

The object is to obtain weighted Steffensen type inequalities for the class of convex functions using inequalities for the class of functions that are "convex at point $c$''. Additionally, we give weaker conditions for obtained weighted Steffensen type inequalities. Moreover, by further generalizations of these inequalities we obtain refined and sharpened versions.

References

  • [1] S. N. Bernstein, Sur les fonctions absolument monotones, Acta Math. Vol:52 (1929), 1–66.
  • [2] J. Jaksetic, J. Pecaric, K. Smoljak Kalamir, Measure theoretic generalization of Peˇcari´c, Mercer and Wu-Srivastava results, Sarajevo J. Math. Vol:12, No.24 (2016), 33–49.
  • [3] Z. Liu, On extension of Steffensen’s inequality, J. Math. Anal. Approx. Theory Vol:2, No.2 (2007), 132–139.
  • [4] P. R. Mercer, Extensions of Steffensen’s inequality, J. Math. Anal. Appl. Vol:246, No.1 (2000), 325–329.
  • [5] J. Pecaric Notes on some general inequalities, Publ. Inst. Math. (Beograd), Nouvelle serie Vol:32, No.46 (1982), 131–135.
  • [6] J. Pecaric, A. Perusic, K. Smoljak, Mercer and Wu-Srivastava generalisations of Steffensen’s inequality, Appl. Math. Comput. Vol:219, No.21 (2013), 10548–10558.
  • [7] J. Pecaric, K. Smoljak Kalamir, Generalized Steffensen type inequalities involving convex functions, J. Funct. Spaces Vol:2014, Article ID 428030, 10 pages.
  • [8] J. Pecaric, K. Smoljak, Steffensen type inequalities involving convex functions, Math. Inequal. Appl. Vol:18, No.1 (2015), 363–378.
  • [9] J. Pecaric, K. Smoljak Kalamir, S. Varosanec, Steffensen’s and related inequalities (A comprehensive survey and recent advances), Monograhps in inequalities 7, Element, Zagreb, 2014.
  • [10] J. F. Steffensen, On certain inequalities between mean values and their application to actuarial problems, Skand. Aktuarietids. (1918), 82–97.
  • [11] S. H. Wu, H. M. Srivastava, Some improvements and generalizations of Steffensen’s integral inequality, Appl. Math. Comput. Vol:192 (2007), 422-428.
Year 2018, Volume: 6 Issue: 1, 84 - 91, 15.04.2018

Abstract

References

  • [1] S. N. Bernstein, Sur les fonctions absolument monotones, Acta Math. Vol:52 (1929), 1–66.
  • [2] J. Jaksetic, J. Pecaric, K. Smoljak Kalamir, Measure theoretic generalization of Peˇcari´c, Mercer and Wu-Srivastava results, Sarajevo J. Math. Vol:12, No.24 (2016), 33–49.
  • [3] Z. Liu, On extension of Steffensen’s inequality, J. Math. Anal. Approx. Theory Vol:2, No.2 (2007), 132–139.
  • [4] P. R. Mercer, Extensions of Steffensen’s inequality, J. Math. Anal. Appl. Vol:246, No.1 (2000), 325–329.
  • [5] J. Pecaric Notes on some general inequalities, Publ. Inst. Math. (Beograd), Nouvelle serie Vol:32, No.46 (1982), 131–135.
  • [6] J. Pecaric, A. Perusic, K. Smoljak, Mercer and Wu-Srivastava generalisations of Steffensen’s inequality, Appl. Math. Comput. Vol:219, No.21 (2013), 10548–10558.
  • [7] J. Pecaric, K. Smoljak Kalamir, Generalized Steffensen type inequalities involving convex functions, J. Funct. Spaces Vol:2014, Article ID 428030, 10 pages.
  • [8] J. Pecaric, K. Smoljak, Steffensen type inequalities involving convex functions, Math. Inequal. Appl. Vol:18, No.1 (2015), 363–378.
  • [9] J. Pecaric, K. Smoljak Kalamir, S. Varosanec, Steffensen’s and related inequalities (A comprehensive survey and recent advances), Monograhps in inequalities 7, Element, Zagreb, 2014.
  • [10] J. F. Steffensen, On certain inequalities between mean values and their application to actuarial problems, Skand. Aktuarietids. (1918), 82–97.
  • [11] S. H. Wu, H. M. Srivastava, Some improvements and generalizations of Steffensen’s integral inequality, Appl. Math. Comput. Vol:192 (2007), 422-428.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Josip Pecaric

Ksenija Smoljak Kalamir This is me

Publication Date April 15, 2018
Submission Date June 29, 2017
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Pecaric, J., & Kalamir, K. S. (2018). Weighted Steffensen Type Inequalities Involving Convex Functions. Konuralp Journal of Mathematics, 6(1), 84-91.
AMA Pecaric J, Kalamir KS. Weighted Steffensen Type Inequalities Involving Convex Functions. Konuralp J. Math. April 2018;6(1):84-91.
Chicago Pecaric, Josip, and Ksenija Smoljak Kalamir. “Weighted Steffensen Type Inequalities Involving Convex Functions”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 84-91.
EndNote Pecaric J, Kalamir KS (April 1, 2018) Weighted Steffensen Type Inequalities Involving Convex Functions. Konuralp Journal of Mathematics 6 1 84–91.
IEEE J. Pecaric and K. S. Kalamir, “Weighted Steffensen Type Inequalities Involving Convex Functions”, Konuralp J. Math., vol. 6, no. 1, pp. 84–91, 2018.
ISNAD Pecaric, Josip - Kalamir, Ksenija Smoljak. “Weighted Steffensen Type Inequalities Involving Convex Functions”. Konuralp Journal of Mathematics 6/1 (April 2018), 84-91.
JAMA Pecaric J, Kalamir KS. Weighted Steffensen Type Inequalities Involving Convex Functions. Konuralp J. Math. 2018;6:84–91.
MLA Pecaric, Josip and Ksenija Smoljak Kalamir. “Weighted Steffensen Type Inequalities Involving Convex Functions”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 84-91.
Vancouver Pecaric J, Kalamir KS. Weighted Steffensen Type Inequalities Involving Convex Functions. Konuralp J. Math. 2018;6(1):84-91.
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