Generalizations of Jensen-Steffensen and related integral inequalities for superquadratic functions

Shoshana Abramovich, Slavica Ivelić, Josip Pečarić

Research output: Contribution to journalArticlepeer-review

Abstract

We present integral versions of some recently proved results which improve the Jensen-Steffensen and related inequalities for superquadratic functions. For superquadratic functions which are not convex we get inequalities analogous to the integral Jensen-Steffensen inequality for convex functions. Therefore, we get refinements of all the results which use only the convexity of these functions. One of the inequalities that we obtain for a superquadratic function φ is, where, and, which under suitable conditions like those satisfied by functions of power equal or more than 2, is a refinement of the Jensen-Steffensen-Boas inequality. We also prove related results of Mercer's type.

Original languageEnglish
Pages (from-to)937-949
Number of pages13
JournalCentral European Journal of Mathematics
Volume8
Issue number5
DOIs
StatePublished - 2010

Keywords

  • Convex functions
  • Jensen-Steffensen inequality
  • Superquadratic functions

ASJC Scopus subject areas

  • Mathematics (all)

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