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Abstract <p> In the paper, we prove criteria for convexity and concavity of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation>-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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\displaystyle L^{p}\)</EquationSource> </InlineEquation>-norm. Then we compute in quadratures all functions <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> satisfying these criteria. </p>

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Convexity and Concavity of \(\boldsymbol f\)-Potentials (Kolmogorov Means)

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • V.I. Bakhtin,
  • N.A. Tsarev

摘要

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 \(\displaystyle L^{p}\) -norm. Then we compute in quadratures all functions \(f\) satisfying these criteria.