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Mat. Zametki, 2015, Volume 98, Issue 2, Pages 204–220 (Mi mz10608)  

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00079
This work was supported by the Russian Science Foundation under grant 14-11-00079.


DOI: https://doi.org/10.4213/mzm10608

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

Bibliographic databases:

UDC: 517.51
Received: 16.09.2014

Citation: M. A. Guzev, A. A. Dmitriev, “On the Critical Points of the Kolmogorov Mean with Constraints on the Mean of the Arguments”, Mat. Zametki, 98:2 (2015), 204–220; Math. Notes, 98:2 (2015), 237–250

Citation in format AMSBIB
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