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Approximation by interpolating polynomials in Smirnov-Orlicz class
Ramazan Akg\,Daniyal M. Israfilov 대한수학회 2006 대한수학회지 Vol.43 No.2
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) $.