Optimal bounds for the Neuman-Sandor means in terms of geometric and contra-harmonic means

2012/10/15 by Tie-Hong Zhao, Tie‐Hong Zhao, Yu‐Ming Chu +5
Mathematics · #26E60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #G.1.6 #Mathematical Inequalities and Applications #Nonlinear Partial Differential Equations #acm:26E60 #math.CA #msc:26E60

paper · pdf · doi:10.48550/arxiv.1210.3874

6 pages

arxiv created 2012/10/15 · openalex publication_date 2012/10/15 · arxiv updated 2012/10/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this article, we prove that the double inequality αG(a,b)+(1-α)C(a,b)<M(a,b)<βG(a,b)+(1-β)C(a,b) holds true for all a,b>0 with a≠ b if and only if α≥ 5/9 and β≤ 1-1/[2log(1+√(2))]=0.4327..., where G(a,b),C(a,b) and M(a,b) are respectively the geometric, contra-harmonic and Neuman-Sándor means of a and b.

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