Convexity and concavity of $f$-potentials (Kolmogorov means)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912580886331392 |
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| author | Bakhtin, V. I. Tsarev, N. A. |
| author_facet | Bakhtin, V. I. Tsarev, N. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convexity and concavity of $f$-potentials (Kolmogorov means) Bakhtin, V. I. Tsarev, N. A. Functional Analysis 26E60 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. |
| title | Convexity and concavity of $f$-potentials (Kolmogorov means) |
| topic | Functional Analysis 26E60 |
| url | https://arxiv.org/abs/2411.07659 |