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arXiv · 2411.07659

Convexity and concavity of $f$-potentials (Kolmogorov means)

V. I. Bakhtin·N. A. Tsarev
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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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BibTeXRIS

V. I. Bakhtin, N. A. Tsarev. 2024-11-12. Convexity and concavity of $f$-potentials (Kolmogorov means). https://arxiv.org/abs/2411.07659

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