Uniform Polynomial Approximation of Analytic Functions on a Quasidisk Original Research Article

Let L be an arbitrary quasidisk, and ƒ analytic in G and continuous on Ḡ. We prove two theorems establishing a connection between the sequence of values En(f, Ḡ), n = 1, 2 of best uniform polynomial approximations of the function f on Ḡ and its smoothness properties on the boundary ∂G. Then we apply one of these results to the solution of a problem suggested by Turan concerning the correlation between polynomial and rational approximations on the unit disk.