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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…
No Jackson-type estimates for piecewise -monotone, , trigonometric approximation
Dany Leviatan, Oksana V. Motorna, Igor A. Shevchuk
We say that a function is -monotone, , if and is convex in . Let be continuous and -periodic, and change its…
Interpolatory pointwise estimates for convex polynomial approximation
K. A. Kopotun, D. Leviatan, I. Petrova +1
This paper deals with approximation of smooth convex functions on an interval by convex algebraic polynomials which interpolate at the endpoints of this interval. We call s…
Uniform and pointwise shape preserving approximation (SPA) by algebraic polynomials: an update
K. A. Kopotun, D. Leviatan, I. A. Shevchuk
It is not surprising that one should expect that the degree of constrained (shape preserving) approximation be worse than the degree of unconstrained approximation. However, it tur…
On one estimate of divided differences and its applications
K. A. Kopotun, D. Leviatan, I. A. Shevchuk
We give an estimate of the general divided differences , where some of the 's are allowed to coalesce (in which case, is assumed to be sufficiently smoo…
On some properties of moduli of smoothness with Jacobi weights
K. A. Kopotun, D. Leviatan, I. A. Shevchuk
We discuss some properties of the moduli of smoothness with Jacobi weights that we have recently introduced and that are defined as \[ ω_{k,r}^φ(f^{(r)},t)_{α,β,p} :=\sup_{0\leq h\…