Characterization of homogeneous symmetric monotone bivariate means

Abstract

Abstract In this paper, we introduce a class of bivariate means generated by an integral of a continuous increasing function on ( 0 , + ∞ ) $(0,+\infty)$ . This class of means widens the spectrum of possible means and leads to many easy and interesting mean-inequalities. We show that this class of means characterizes the large class of homogeneous symmetric monotone means.

Keywords

• bivariate mean
• differential equation
• intrinsic function