• Korean Journal of Mathematics
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• v.30 no.2
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• pp.305-313
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• 2022

In this paper we consider a modified version of Smirnov operator and obtain some Bernstein-type inequalities preserved by this operator. In particular, we prove some results which in turn provide the compact generalizations of some well-known inequalities for polynomials.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.55-61
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• 2023

In this paper we establish a generalization of a result recently proved by Ganenkova and Starkov [J. Math. Anal. Appl., 476 (2019), 696-714] concerning a modified version of Smirnov operator.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.413-424
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• 2006

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