I. Shevchuk

activity

20172020

most citedUniform and pointwise shape preserving approximation (SPA) by algebraic polynomials: an update

1 citations · 1 across the 5 of their papers we have counts for

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math.CA2017

Interpolatory pointwise estimates for monotone polynomial approximation

K. A. Kopotun, D. Leviatan, I. A. Shevchuk

Given a nondecreasing function $f$ on $[- 1, 1]$ , we investigate how well it can be approximated by nondecreasing algebraic polynomials that interpolate it at $\pm 1$ . We establish p…

math.CA2017

On weighted approximation with Jacobi weights

Kirill A. Kopotun, Dany Leviatan, Igor A. Shevchuk

We obtain matching direct and inverse theorems for the degree of weighted $L_{p}$ -approximation by polynomials with the Jacobi weights $(1 - x)^{α} (1 + x)^{β}$ . Combined, the estimates yield…