On the Critical Points of the Kolmogorov Mean with Constraints on the Mean of the Arguments

M. A. Guzev, A. A. Dmitriev

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok

Abstract: 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.

UDC: 517.51

Received: 16.09.2014

DOI: 10.4213/mzm10608

 English version: Mathematical Notes, 2015, 98:2, 237–250

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