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

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.