Journal of the
Korean Mathematical Society JKMS

Let $\Gamma $ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let $G:=\operatorname{int}\Gamma $. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_{n}$ for $\overline{G}$ to the function of the reflexive Smirnov-Orlicz class $E_{M}\left( G\right) $ is equivalent to the best approximating polynomial rate in $E_{M}\left( G\right) $.

Keywords: curves of bounded rotation, Faber polynomials, interpolating polynomials, Smirnov-Orlicz class, Orlicz space, Cauchy singular operator

MSC numbers: Primary 41A10, 41A50; Secondary 41A05, 41A25, 30C10, 30C15