K. Kopotun

activity

20112023

most citedUniform and Pointwise Shape Preserving Approximation by Algebraic Polynomials

33 citations · 38 across the 14 of their papers we have counts for

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Showing 2017Show all

3 papers · 1 filter

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…

math.CA2017

On moduli of smoothness with Jacobi weights

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

The main purpose of this paper is to introduce moduli of smoothness with Jacobi weights $(1 - x)^{α} (1 + x)^{β}$ for functions in the Jacobi weighted $L_{p} [- 1, 1]$ , $0 < p \leq \infty$ , spaces.…