Convexity and concavity of f-potentials (Kolmogorov means)

2024/11/12 by V. I. Bakhtin, Bakhtin, V. I., N. A. Tsarev +1
Mathematics · #26E60 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2411.07659

openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we prove criteria for convexity and concavity of f-potentials (f-means, Kolmogorov means, weighted quasi-arithmetic means), which particular cases are the arithmetic, geometric, harmonic means, the thermodynamic potential (exponential mean), and the L^p-norm. Then we compute in quadratures all functions f satisfying these criteria.

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