Journal Article10.1007/BF01057540
J-property of Jordan arcs
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About: This article is published in Ukrainian Mathematical Journal. The article was published on 01 Jan 1989.
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Citations
Jackson's inequality in the complex plane and the Łojasiewicz-Siciak inequality of Green's function
TL;DR: It is proved a generalization of Jackson's inequality for compact sets in the complex plane admitting both upper and lower bounds for their Green's functions, i.e., the well known Holder Continuity Property and the less known but crucial Łojasiewicz-Siciak inequality.
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Jackson's inequality in the complex plane and the Lojasiewicz-Siciak inequality of Green's function
TL;DR: In this paper, a generalization of Dunham Jackson's famous approximation inequality to the case of compact sets in the complex plane admits both upper and lower bounds for their Green's functions, i.e., the Holder Continuity Property (HCP) and the less known but crucial Lojasiewicz-Siciak inequality (LS).
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Polynomial Approximation on Compact Sets Bounded by Dini-Smooth Arcs
Leonhard Frerick,Jürgen Müller +1 more
TL;DR: For compact sets which are not the closure of a Jordan domain, the Faber operator provides a well-known tool for deriving results on the error of uniform polynomial approximation on K.
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An approximation problem with a new characteristic and a problem on mean approximation on arcs in a complex plane
TL;DR: In this article, classical approximation theorems are investigated on the curves in a complex domain, and direct and inverse theoremologies are cited on the curve Γ in the complex domain in the metric Lp(Γ).
Harmonic Version of Jackson's Theorem in the Complex Plane
TL;DR: The classical Jackson theorem concerning polynomial approximation of functions on?1, 1] is generalized to the case of functions given on a piecewise smooth arc in the complex plane by harmonic polynomials.