Periodica Mathematica Hungarica

, Volume 55, Issue 1, pp 19–34 | Cite as

On the Jensen-Steffensen inequality for generalized convex functions

  • M. Klaričić BakulaEmail author
  • A. Matković
  • J. Pečarić


Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

Key words and phrases

P-convex functions functions with nondecreasing increments Jensen-Steffensen inequality Čebyšev’s inequality Hölder’s inequality generalized quasiarithmetic means 

Mathematics subject classification number

26D15 26B25 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • M. Klaričić Bakula
    • 1
    Email author
  • A. Matković
    • 2
  • J. Pečarić
    • 3
  1. 1.Department of Mathematics, Faculty of Natural Sciences, Mathematics and EducationUniversity of SplitSplitCroatia
  2. 2.Faculty of Electrical Engineering, Mechanical Engineering and Naval ArchitectureUniversity of SplitSplitCroatia
  3. 3.Faculty of Textile TechnologyUniversity of ZagrebZagrebCroatia

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