On harmonic representation of means

2013/10/11 by Alfred Witkowski, Witkowski, Alfred
Mathematics · #26D15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CA #msc:26D15

paper · pdf · doi:10.48550/arxiv.1310.3063

arxiv created 2013/10/11 · openalex publication_date 2013/10/11 · arxiv updated 2013/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize continuous, symmetric and homogeneous means M that can be represented in the form (1)/(M(x,y))=∫₀¹ \fracdtN(\tfracx+y2-t\tfracx-y2,\tfracx+y2+t\tfracx-y2). New inequalities for means are derived from such representation.

Related

• On Some Integral Means
• A Note on the Weighted Harmonic-Geometric-Arithmetic Means Inequalities
• Means refinements via convexity
• Refinement of Inequalities among Means
• Expansion of a bivariate symmetric mean in the neighborhood of the first bisector