AIMS Mathematics, 2021, 6(1): 296-303. doi: 10.3934/math.2021018.

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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

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.
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Keywords 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. AIMS Mathematics, 2021, 6(1): 296-303. doi: 10.3934/math.2021018

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