On the best hardy constant for quasi–arithmetic means and homogeneous deviation means

Z. Páles, Pawe Pasteczka

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4 Citations (Scopus)


The aim of this paper is to characterize the so-called Hardy means, i.e., those means M:? n=1 Rn + ? R+ that satisfy the inequality ? ? ? M(x1,...,xn) C ? xn n=1 n=1 for all positive sequences (xn) with some finite positive constant C. The smallest constant C satisfying this property is called the Hardy constant of the mean M. In this paper we determine the Hardy constant in the cases when the mean M is either a concave quasi-arithmetic or a concave and homogeneous deviation mean.

Original languageEnglish
Pages (from-to)585-599
Number of pages15
JournalMathematical Inequalities and Applications
Issue number2
Publication statusPublished - Apr 1 2018



  • Deviation mean
  • Gini mean
  • Hardy constant
  • Hardy inequality
  • Hardy mean
  • Mean
  • Quasi-arithmetic mean

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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