F. G. Abdullayev

On the convergence of bieberbach polynomials in domains with interior zero angles

Let G⊂C be a finite Jordan domain, 0εG and w = φ(z) be the conformal mapping of G onto a disc normalized by . It is well known that the uniform convergence of Bieberbach polynomials for the pair (G, 0) to φ(z) in Ǥ is governed by the properties of ∂G. In this study, the decrease of to zero and the estimation of this error in domains with interior zero angles are determined depending on the properties of boundary arcs and the degree of their touch.

ON THE GROWTH OF ALGEBRAIC POLYNOMIALS IN THE WHOLE COMPLEX PLANE

In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior and exterior zero angles.

An analogue of the Bernstein-Walsh lemma in Jordan regions of the complex plane

In this paper we continue to study two-dimensional analogues of Bernstein-Walsh estimates for arbitrary Jordan domains.MSC:Primary 30A10; 30C10; secondary 41A17.

On the Uniform Convergence of the Generalized Bieberbach Polynomials in Regions with K-Quasiconformal Boundary

AbstractLet G be a finite domain in the complex plane with K-quasicon formal boundary, z0be an arbitrary fixed point in G and p>0. Let π(z) be the conformal mapping from G onto the disk with radius r0>0 and centered at the origin 0, normalized by ϕ(z0) = 0 and ϕ(z0) = 1. Let us set

Uniform Convergence of Some Extremal Polynomials in Domain with Corners on the Boundary

\varphi _p \left( z \right): = \int_{x_0 }^x {\left[ {\phi \left( \zeta \right)} \right]^{2/8} } d\zeta

Solutions of the rational difference equations xn+1=xn−111+xn−2xn−5xn−8

, and let πn,p(z) be the generalized Bieberbach polynomial of degree n for the pair (G,z0) that minimizes the integral

METRIC SPACES WITH UNIQUE PRETANGENT SPACES. CONDITIONS OF THE UNIQUENESS

\iint\limits_c {\left| {\varphi _p \left( z \right) - P_x^1 (z)} \right|^p d0_x }