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

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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 holds for all \({x,y\in I}\). In this paper, we investigate the equality and comparison problem in the class of .

*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$$K(x,y)=\varphi^{-1}(p\varphi(x)+q\varphi(y)+(1-p-q)\varphi(M(x,y)))=:M_ \varphi^{(p,q)}(x,y)$$

*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

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