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Generalizations of the Jensen-Steffensen and related inequalities

  • Milica Klaričić Bakula
  • Marko Matić
  • Josip Pečarić
Research Article
  • 60 Downloads

Abstract

We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.

Keywords

Convex functions Jensen-Steffensen inequality Slater’s inequality 

MSC

26D15 

References

  1. [1]
    Abramovich S., Klaričić Bakula M., Matić M., Pečarić J., A variant of Jensen-Steffensen’s inequality and quasi-arithmetic means, 2005, J. Math. Anal. Appl., 307, 370–386zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Boas R.P., The Jensen-Steffensen inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 1970, 302–319, 1–8MathSciNetGoogle Scholar
  3. [3]
    Dragomir S.S., Goh C.J., A counterpart of Jensen’s discrete inequality for differentiable convex mappings and applications in information theory, Math. Comput. Modelling, 1996, 24(2), 1–11zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Dragomir S.S., On a converse of Jensen’s inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 2001, 12(2), 48–51zbMATHMathSciNetGoogle Scholar
  5. [5]
    Dragomir S.S., Ionescu N.M., Some converse of Jensen’s inequality and applications, Rev. Anal. Numér. Théor. Approx., 1994, 23(1), 71–78zbMATHMathSciNetGoogle Scholar
  6. [6]
    Elezović N., Pečarić J., A counterpart to Jensen-Steffensen’s discrete inequality for differentiable convex mappingsand applications in information theory, Rad Hrvat. Akad. Znan. Umjet., 2003, 481(14), 25–28Google Scholar
  7. [7]
    Matić M., Pečarić J., Some companion inequalities to Jensen’s inequality, Math. Inequal. Appl., 2000, 3(3), 355–368zbMATHMathSciNetGoogle Scholar
  8. [8]
    Pečarić J., A companion to Jensen-Steffensen’s inequality, J. Approx. Theory, 1985, 44(3), 289–291zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Pečarić J., A multidimensional generalization of Slater’s inequality, J. Approx. Theory, 1985, 44(3), 292–294zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Roberts A.W., Varberg D.E., Convex functions, Academic Press, New York-London, 1973zbMATHGoogle Scholar
  11. [11]
    Slater M.L., A companion inequality to Jensen’s inequality, J. Aprox. Theory, 1981, 32(2), 160–166zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Steffensen J.F., On certain inequalities and methods of approximation, J. Inst. Actuaries, 1919, 51, 274–297Google Scholar

Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Milica Klaričić Bakula
    • 1
  • Marko Matić
    • 1
  • Josip Pečarić
    • 2
  1. 1.Faculty of Science, Department of MathematicsUniversity of SplitSplitCroatia
  2. 2.Faculty of Textile TechnologyUniversity of ZagrebZagrebCroatia

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