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March 29, 2026Russian Journal of Mathematical Physics0 citations

Convexity and Concavity of f-Potentials (Kolmogorov Means)

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VBV.I. BakhtinNTN.A. Tsarev

Key Points

  • The aim is to establish criteria for the convexity and concavity of f-potentials, including specific means.
  • Develop theoretical criteria for assessing convexity and concavity
  • Analyze specific cases of f-potentials like arithmetic and geometric means
  • Compute necessary functions that meet established criteria using quadratures
  • Criteria for convexity and concavity of f-potentials were successfully proven
  • Specific cases such as the arithmetic, harmonic, and thermodynamic potentials were analyzed
  • Functions satisfying these convexity and concavity criteria were computed explicitly

Abstract

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

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Cite This Study

Bakhtin et al. (2026) studied this question.

synapsesocial.com/papers/69c8c25dde0f0f753b39ca6fhttps://doi.org/10.1134/s1061920825601351
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