Geodesic
On the Critical Points of the Kolmogorov Mean with Constraints on the Mean of the Arguments
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 204-220.

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We study the critical points of the Kolmogorov mean under constraints on the arithmetic mean of the arguments. We establish that, in this case, the topology of the critical points is the same for all classes of functions whose derivative determines a convex involution; the critical points themselves coincide for all functions with coinciding involutions. These claims can be used when analyzing modeling results for physical systems under various choices of the functions parameterizing the internal structure of these systems.
Keywords: Kolmogorov mean, convex function, critical point, Maslov's axiom. 
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M. A. Guzev; A. A. Dmitriev. On the Critical Points of the Kolmogorov Mean with Constraints on the Mean of the Arguments. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 204-220. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a5/

[1] V. P. Maslov, “O nelineinosti osrednenii v finansovoi matematike”, Matem. zametki, 74:6 (2003), 944–947 | DOI | MR | Zbl

[2] V. P. Maslov, “Nelineinoe srednee v ekonomike”, Matem. zametki, 78:3 (2005), 377–395 | DOI | MR | Zbl

[3] V. P. Maslov, Kvantovaya ekonomika, Nauka, M., 2006

[4] A. N. Kolmogorov, “Ob opredelenii srednego”, Izbranye trudy. Matematika i mekhanika, Nauka, M., 1985, 136–138

[5] M. A. Guzev, A. A. Dmitriev, “Bifurkatsionnoe povedenie potentsialnoi energii sistemy chastits”, Fizicheskaya mezomekhanika, 16:3 (2013), 27–33

[6] M. A. Guzev, A. A. Dmitriev, “Peremezhaemost spektra matritsy, imeyuschei blochnuyu strukturu”, Matematika v prilozheniyakh, Vserossiiskaya konferentsiya, priurochennaya k 80-ti letiyu akademika S. K. Godunova (Novosibirsk, 20–24 iyulya 2009 g.), Tezisy dokladov, In-t matem. SO RAN, Novosibirsk, 2009, 98–99

[7] S. Pashkovskii, Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983 | MR | Zbl