On a class of Bivariate means including a lot of old and new means

Mustapha Ra\; Anis Rezgui

doi:10.4134/CKMS.c180062

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

QR
Code

Article

HOME

ALL ARTICLES

View

Commun. Korean Math. Soc. 2019; 34(1): 239-251

Online first article January 14, 2019 Printed January 31, 2019

https://doi.org/10.4134/CKMS.c180062

On a class of Bivariate means including a lot of old and new means

Mustapha Ra\"{\i}ssouli, Anis Rezgui

Moulay Ismail University; Carthage University

Abstract

Go to

Abstract

In this paper we introduce a new formulation of symmetric homogeneous bivariate means that depends on the variation of a given continuous strictly increasing function on $(0,\infty)$. It turns out that this class of means includes a lot of known bivariate means among them the arithmetic mean, the harmonic mean, the geometric mean, the logarithmic mean as well as the first and second Seiffert means. Using this new formulation we introduce a lot of new bivariate means and derive some mean-inequalities.

Keywords: bivariate mean, functional equation, mean-inequalities

MSC numbers: 26E60