Inequalities for averages of quasiconvex and superquadratic functions

S. Abramovich, L. E. Persson

Research output: Contribution to journalArticlepeer-review


For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1i=0 f(ai/an-1)-1/an+1nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1i=0 f(ai/an-1)-1/an+1nηi=0f(ai/an) are also included.

Original languageEnglish
Pages (from-to)535-550
Number of pages16
JournalMathematical Inequalities and Applications
Issue number2
StatePublished - Apr 2016


  • Convexity
  • Differences of averages
  • Inequalities
  • Lower bounds.
  • Refinements
  • Superquadracity
  • γ-quasiconvexity

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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