Sharp bounds for the difference between the arithmetic and geometric means

2012/03/20 by J. M. Aldaz, Aldaz, J. M. · 1 citation
Mathematics · #26D15 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.1203.4454

openalex publication_date 2012/03/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We present sharp bounds for ∑_i=1ⁿ α_i x_i - ∏_i=1ⁿ x_i^α_i in terms of the variance of the vector (x₁^1/2,...,x_n^1/2).

Citations

• Bounds for the normalised Jensen functional

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• A monotonicity property of variances

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