Geodesic
The Problem of Approximation in Mean on Arcs in the Complex Plane
Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 698-714

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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. 
@article{MZM_2016_99_5_a5,
     author = {J. I. Mamedkhanov},
     title = {The {Problem} of {Approximation} in {Mean} on {Arcs} in the {Complex} {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {698--714},
     publisher = {mathdoc},
     volume = {99},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a5/}
}
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J. I. Mamedkhanov. The Problem of Approximation in Mean on Arcs in the Complex Plane. Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 698-714. http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a5/