Best constants for approximations of periodic functions by Fejér operators

We obtain the best estimate for approximations of continuous 2-periodic functions by Fejér summation operators. The estimate is expressed in terms of the moduli of continuity of functions to be approximated. In the class of functions satisfying Lipschitz condition, we obtain the best constant for the approximation by Fejer integral and summation operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 75–82, 1990.     

Reducibility of nonlinear almost periodic systems of difference equations given on a torus

We establish sufficient conditions for a nonlinear system of difference equations x(t + 1) =x(t) + + P(x(t),t)+ to be reducible to the system y(t + 1) =y(t) + . Here, P(x, t) is a function 2-periodic in x_i(i = 1, ...,n) and almost periodic int with a frequency basis .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 404–412, April, 1994.This work was supported by Ukrainian State Committee on Science and Technology.     

Comparison Principle Based on Minkowski Mixed Volumes for a Family of Differential Equations

A comparison principle based on Minkowski mixed volumes is established for a family of differential equations with imprecise parameter values. Scalar and vector approaches are considered, and the basic inequalities of the comparison principle are established.     

On the stability of a set of systems of impulsive equations

Doklady Mathematics -     

Second bogolyubov theorem for systems of difference equations

We establish an analog of the second Bogolyubov theorem for a system of difference equations.