On uniform polynomial approximation of functions that are analytic in finite number of non-intersecting continuums

We show that some of results, obtained by S.N. Bernstein, on constructive function theory, under certain conditions, take place for uniform polynomial approximation of functions that are analytic in finite number of non-intersecting continuums. On the base of obtained results for certain class of analytic functions we calculate asymptotic values of some $n$-widths.

Chebyshev polynomials and best approximation of some classes of functions

In this research using properties of Chebyshev polynomialswe explicitly determine the best uniform polynomial approximation of some classes of functions. In this way we present some new theorems about the best approximation of these classes.