2019
Том 71
№ 6

# Imash kyzy M.

Articles: 2
Article (English)

### Polynomial inequalities in regions with interior zero angles in the Bergman space

Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 318-336

We investigate the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space $A_p(G, h),\; p > 0$, in regions with interior zero angles at finitely many boundary points. We obtain estimations for algebraic polynomials in bounded regions with piecewise smooth boundary.

Article (Ukrainian)

### Application of the Faber polynomials in proving combinatorial identities

Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 151-164

We study the possibility of application of the Faber polynomials in proving some combinatorial identities. It is shown that the coefficients of Faber polynomials of mutually inverse conformal mappings generate a pair of mutually invertible relations. We prove two identities relating the coefficients of Faber polynomials and the coefficients of Laurent expansions of the corresponding conformal mappings. Some examples are presented.