Sharp power means bounds for Neuman-Sándor mean

2012/08/04 by Zhen-Hang Yang, Yang, Zhen-Hang
Mathematics · #26E60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CA #msc:26E60

paper · pdf · doi:10.48550/arxiv.1208.0895

10 pages

arxiv created 2012/08/04 · openalex publication_date 2012/08/04 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a,b>0 with a\not=b, let N(a,b) denote the Neuman-Sándor mean defined by N(a,b)=((a-b)/(2arcsinh((a-b)/(a+b)))) and A_r(a,b) denote the r-order power mean. We present the sharp power means bounds for the Neuman-Sándor mean: A_p1(a,b)<N(a,b)\leqA_p2(a,b), where p₁= ((ln2)/(lnln(3+2\surd2))) and p₂=4/3 are the best constants.

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