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On the growth of mth derivatives of algebraic polynomials in the weighted Lebesgue space

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

In this paper, we study the growth of the mth derivative of an arbitrary algebraic polynomial in bounded and unbounded general domains of the complex plane in weighted Lebesgue spaces. Further, we obtain estimates for the derivatives at the closure of this regions. As a result, estimates for derivatives on the entire complex plane were found.

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Exact estimates for Faber polynomials and for norm of Faber operator

Fahreddin ABDULLAYEV

Exact estimates for Faber polynomials, norm of Faber operator, and -norm of the generating function for the sequence of Faber operator of univalent functions of class sigma are found. The description of continua of the complex plane for which the norm of Faber operator take the value 1 or 3 is obtained.

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Approximate properties of the p-Bieberbach polynomials in regions with simultaneously exterior and interior zero angles

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

In this paper, we study the uniform convergence ofp-Bieberbach polynomials in regions with a finite number of both interior and exterior zero angles at the boundary.

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