Normalized jensen functional, superquadracity and related inequalities

Shoshana Abramovich, Silvestru S. Dragomir

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this paper we generalize the inequality (Formula Presented) where (Formula Presented) obtained by S.S. Dragomir for convex functions. We show that for the class of functions that we call superquadratic, strictly positive lower bounds of Jn (f, x, p)—mJn (f, x, q) and strictly negative upper bounds of Jn (f, x, p)-MJn (f, x, q) exist when the functions are also nonnegative. We also provide cases where we can improve the bounds m and M for convex functions and superquadratic functions. Finally, an inequality related to the Čebyšev functional and superquadracity is also given.

Original languageEnglish
Title of host publicationInternational Series of Numerical Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
StatePublished - 2009

Publication series

NameInternational Series of Numerical Mathematics
ISSN (Print)0373-3149
ISSN (Electronic)2296-6072

Bibliographical note

Publisher Copyright:
© Birkhäuser Verlag Basel/Switzerland 2008.


  • Convex functions
  • Jensen Steffensen inequality
  • Jensen inequality
  • Superquadratic functions
  • Čebyšev inequality

ASJC Scopus subject areas

  • Numerical Analysis
  • Control and Optimization
  • Applied Mathematics


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