Hermite-Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions

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Abstract

In this paper we prove some Hermite-Hadamard, Fejer and Sherman type inequlities for generalizations of superquadratic functions and convex functions. These results, under a monotonicity condition, lead to refinements of the Hermite-Hadamard, Fejer and Sherman inequalities of non-negative convex functions. Also, the obtained inequalities are discussed about and compared with some recent generalizations of weighted Hermite-Hadamard inequalities.

Original languageEnglish
Pages (from-to)559-575
Number of pages17
JournalJournal of Mathematical Inequalities
Volume14
Issue number2
DOIs
StatePublished - 1 Jun 2020

Bibliographical note

Publisher Copyright:
© Zagreb.

Keywords

  • Convexity
  • f-divergence
  • Fejer type inequalities
  • Hermite-hadamard type inequalities
  • Jensen type inequalities
  • N -quasiconvexity
  • N -quasisuperquadracity
  • Sherman type inequalities
  • Superquadracity

ASJC Scopus subject areas

  • Analysis

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