Abstract. We extend the results on the uniform convergence of Bieberbach polynomials to domains with certain interior zero angles (outward pointing cusps), and show that they play a special role inâ€¦ (More)

â€“ We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, k 1) for analytic functions defined on a continuum E in the complex plane, which simultaneouslyâ€¦ (More)

This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods andâ€¦ (More)

We establish weighted L p, 1 â‰¤ p < âˆž Bernstein-, Remez-, Nikolskii-, and Marcinkiewicz-type inequalities for algebraic polynomials considered on a quasismooth (in the sense of Lavrentiev) arc in theâ€¦ (More)

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functionsâ€¦ (More)

For an arbitrary continuum in the complex plane with connected complement we study the rate of its approximation from outside by lemnis-cates in terms of level lines of a conformal mapping of ontoâ€¦ (More)