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Matematicheskie Zametki, 2016, Volume 99, Issue 5, Pages 698–714
DOI: https://doi.org/10.4213/mzm9287 (Mi mzm9287) 		 
The Problem of Approximation in Mean on Arcs in the Complex Plane

J. I. Mamedkhanov

Baku State University
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DOI: https://doi.org/10.4213/mzm9287
Abstract: Classical theorems on the approximation of curves in the complex domain are studied; in particular, direct and inverse theorems on the arcs $\Gamma$ in the complex plane in the metric of $L_p(\Gamma)$ are obtained. The results obtained are new in the case of a closed interval $[-1,1]$ as well.
Keywords: approximation of curves in the complex domain, Jackson–Bernstein theorem, Lipschitz condition, Newman problem, Jordan curve, Jackson–Dzyadyk polynomial, Minkowski inequality.
Received: 25.11.2011
Revised: 02.08.2013
English version:
Mathematical Notes, 2016, Volume 99, Issue 5, Pages 697–710
DOI: https://doi.org/10.1134/S0001434616050084
Bibliographic databases:
Document Type: Article
UDC: 517.551
Language: Russian
Citation: J. I. Mamedkhanov, “The Problem of Approximation in Mean on Arcs in the Complex Plane”, Mat. Zametki, 99:5 (2016), 698–714; Math. Notes, 99:5 (2016), 697–710
Citation in format AMSBIB
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