Convexity and concavity of f-potentials (Kolmogorov means)
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 Lp-norm. Then we compute in quadratures all functions f satisfying these criteria.
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