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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Showing 2020Show all

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math.CA2020

Exact pointwise estimates for polynomial approximation with Hermite interpolation

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

We establish best possible pointwise (up to a constant multiple) estimates for approximation, on a finite interval, by polynomials that satisfy finitely many (Hermite) interpolatio…

math.CA2020

No Jackson-type estimates for piecewise $q$ -monotone, $q \geq 3$ , trigonometric approximation

Dany Leviatan, Oksana V. Motorna, Igor A. Shevchuk

We say that a function $f \in C [a, b]$ is $q$ -monotone, $q \geq 3$ , if $f \in C^{q - 2} (a, b)$ and $f^{(q - 2)}$ is convex in $(a, b)$ . Let $f$ be continuous and $2 π$ -periodic, and change its…

math.CA2020

Interpolatory pointwise estimates for convex polynomial approximation

K. A. Kopotun, D. Leviatan, I. Petrova +1

This paper deals with approximation of smooth convex functions $f$ on an interval by convex algebraic polynomials which interpolate $f$ at the endpoints of this interval. We call s…

Exact pointwise estimates for polynomial approximation with Hermite interpolation

No Jackson-type estimates for piecewise q-monotone, q≥3, trigonometric approximation

Interpolatory pointwise estimates for convex polynomial approximation

No Jackson-type estimates for piecewise $q$ -monotone, $q \geq 3$ , trigonometric approximation