APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS

Title & Authors
APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS
Akgun Ramazan; Israfilov Daniyal M.;

Abstract
Let $\small{\Gamma}$ be a bounded rotation (BR) curve without cusps in the complex plane $\small{\mathbb{C}}$ and let G := int $\small{\Gamma}$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $\small{F_n\;for\;\bar G}$ to the function of the reflexive Smirnov-Orlicz class $\small{E_M (G)}$ is equivalent to the best approximating polynomial rate in $\small{E_M (G)}$.
Keywords
curves of bounded rotation;Faber polynomials;interpolating polynomials;Smirnov-Orlicz class;Orlicz space;Cauchy singular operator;
Language
English
Cited by
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2.
Approximating Polynomials for Functions of Weighted Smirnov-Orlicz Spaces, Journal of Function Spaces and Applications, 2012, 2012, 1
3.
On approximation in weighted Smirnov–Orlicz classes, Complex Variables and Elliptic Equations, 2012, 57, 5, 567
4.
Approximation by polynomials and rational functions in weighted rearrangement invariant spaces, Journal of Mathematical Analysis and Applications, 2008, 346, 2, 489
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