Necessary and sufficient conditions on the Schur convexity of a bivariate mean

Hong-Ping Yin; Xi-Min Liu; Jing-Yu Wang; Bai-Ni Guo; Hong-Ping Yin; Xi-Min Liu; Jing-Yu Wang; Bai-Ni Guo

doi:10.3934/math.2021018

AIMS Mathematics

2021, Volume 6, Issue 1: 296-303. doi: 10.3934/math.2021018

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Research article

Necessary and sufficient conditions on the Schur convexity of a bivariate mean

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China
2.
College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
3.
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China

Received: 01 June 2020 Accepted: 30 September 2020 Published: 10 October 2020
MSC : Primary 26E60; Secondary 26A51, 26D15, 26D20, 41A55

In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.
- necessary and sufficient condition,
- bivariate mean,
- Schur convex function,
- Schur harmonically convex function,
- inequality,
- majorization
Citation: Hong-Ping Yin, Xi-Min Liu, Jing-Yu Wang, Bai-Ni Guo. Necessary and sufficient conditions on the Schur convexity of a bivariate mean[J]. AIMS Mathematics, 2021, 6(1): 296-303. doi: 10.3934/math.2021018

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Abstract

In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.

References

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