Aequationes mathematicae

, Volume 81, Issue 3, pp 201–208

On the equality and comparison problem of a class of mean values

Article

DOI: 10.1007/s00010-011-0074-1

Cite this article as:
Daróczy, Z. Aequat. Math. (2011) 81: 201. doi:10.1007/s00010-011-0074-1

Abstract

Let \({I\subset \mathbb {R}}\) be a nonvoid open interval. A function \({K:I^2\to I}\) is called an M-conjugate mean if there exists \({(p,q)\in [0,1]^2}\) and a continuous strictly monotone real valued function \({\varphi}\) on I such that
$$K(x,y)=\varphi^{-1}(p\varphi(x)+q\varphi(y)+(1-p-q)\varphi(M(x,y)))=:M_ \varphi^{(p,q)}(x,y)$$
holds for all \({x,y\in I}\). In this paper, we investigate the equality and comparison problem in the class of M-conjugate means, in the case when
$$M(x,y):=\min\{x,y\}\quad (x,y\in I)$$
.

Mathematics Subject Classification (2000)

39B22

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary