Comparison theorems and some of their applications

Analogues of Kolmogorov comparison theorems and some of their applications were established.Comment: 6 pages in English and Russian. arXiv admin note: substantial text overlap with arXiv:1309.655

On a general approach to some problems of approximation of operators

In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in the area of Ostrowski type inequalities can be obtained by standard arguments

Kolmogorov\u27s Problem for Completely and Multiply Monotone Functions and the Markov Moment Problem

In this paper, we present the solution to Kolmogorov’s problem for the classes of multiply monotone and completely monotone functions together with its connections to the Markov moment problem, Hermite-Birkhoff interpolation problem, and other extremal problems