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.
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