On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means

Abstract

The aim of this paper is to characterize the so-called Hardy means, i.e., those means $M:{\bigcup }_{n=1}^{\infty }{\mathbb{R}}_{+}^n\to {\mathbb{R}}_{+}$ that satisfy the inequality $$\sum _{n=1}^{\infty }M(x_1,\dots ,x_n)\le C\sum _{n=1}^{\infty }{x}_n$$ for all positive sequences $(x_n)$ 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.

Math. Inequal. Appl. 2018

References in corpus (1)

• Characterization of the Hardy property of means and the best Hardy constants

Cited by in corpus (6)

• On Kedlaya type inequalities for weighted means
• On the homogenization of means
• On Hardy type inequalities for weighted quasideviation means
• Weakening of Hardy property for means
• On properties of weighted Hardy constant for means
• On the integral approach to means and their Hardy property