Schur-$m$ power convexity of Cauchy means and its application

Dong-Sheng Wang; Chunru Fu; Huannan Shi

doi:10.1216/rmj.2020.50.1859

Abstract

Necessary and sufficient conditions for the Cauchy mean value to be Schur- $m$ power convex or concave are given. As applications, Schur- $m$ power convexity of the exponential mean is discussed, and a comparative inequality between the Gini mean and the Stolarsky mean is given.

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Dong-Sheng Wang. Chunru Fu. Huannan Shi. "Schur-$m$ power convexity of Cauchy means and its application." Rocky Mountain J. Math. 50 (5) 1859 - 1869, October 2020. https://doi.org/10.1216/rmj.2020.50.1859

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Received: 7 December 2019; Revised: 7 April 2020; Accepted: 18 May 2020; Published: October 2020

First available in Project Euclid: 5 November 2020

zbMATH: 07274842

MathSciNet: MR4170694

Digital Object Identifier: 10.1216/rmj.2020.50.1859

Subjects:

Primary: 26A51‎ , 26D15 , 26E60 , 34K38

Keywords: Cauchy mean , exponential mean , majorization , Schur-$m$ power convexity

Abstract

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