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.
Bakhtin et al. (2026) studied this question.