Sharp inequalities for the Neuman-Sandor mean in terms of arithmetic and contra-harmonic means

2012/09/26 by Miao-Kun Wang, Yu‐Ming Chu, Wang, Miao-Kun +5
Mathematics · #26E20 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #G.1.6 #Mathematical Inequalities and Applications #Nonlinear Partial Differential Equations #acm:26E20 #math.CA #msc:26E20

paper · pdf · doi:10.48550/arxiv.1209.5825

9 pages

arxiv created 2012/09/26 · openalex publication_date 2012/09/26 · arxiv updated 2012/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we find the greatest values α and λ, and the least values β and μ such that the double inequalities C^α(a,b)A^1-α(a,b)<M(a,b)<C^β(a,b)A^1-β(a,b) and &[C(a,b)/6+5 A(a,b)/6]^λ[C^1/6(a,b)A^5/6(a,b)]^1-λ<M(a,b) & <[C(a,b)/6+5 A(a,b)/6]^μ[C^1/6(a,b)A^5/6(a,b)]^1-μ hold for all a,b>0 with a≠ b, where M(a,b), A(a,b) and C(a,b) denote the Neuman-Sándor, arithmetic, and contra-harmonic means of a and b, respectively.

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