Approximation of classes of operators of special type (Q2880024)

The asymptotic equality for the least upper bounds of the deviations of a special type of operators is considered in the uniform metric on the classes of functions defined on the real axis and, not necessarily periodic, where derivatives belong to the unit ball of the space of essentially bounded functions. In some cases, the resulting equation gives the solution of Kolmogorov-Nikolski. Conditions for increasing and decreasing functions are obtained.