33 citations · 38 across the 14 of their papers we have counts for
6 papers · 1 filter
New moduli of smoothness
K. A. Kopotun, D. Leviatan, I. A. Shevchuk
In this paper, we discuss various properties of the new modulus of smoothness \[ ω^φ_{k,r}(f^{(r)},t)_p := \sup_{0 < h\leq t}\|\mathcal W^r_{kh}(\cdot) Δ_{hφ(\cdot)}^k (f^{(r)},\cd…
Polynomial approximation with doubling weights having finitely many zeros and singularities
Kirill A. Kopotun
We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights having finitely many zeros and singularities (i.e., points where $w…
New moduli of smoothness: weighted DT moduli revisited and applied
K. A. Kopotun, D. Leviatan, I. A. Shevchuk
We introduce new moduli of smoothness for functions , , , that have an st locally absolutely continuous derivative…
Weighted moduli of smoothness of -monotone functions and applications
Kirill A. Kopotun
Let be the Ditzian-Totik modulus with weight , be the cone of -monotone functions on , i.e., those functions whose th divided difference…
Polynomial approximation with doubling weights
Kirill A. Kopotun
Among other things, we prove that, for a doubling weight , , , and , we have \[ E_n(f)_{p, w_n} = O(n^{-α}) \iff ω_φ^{r+1}(f,…
Constrained Spline Smoothing
K. Kopotun, D. Leviatan, A. Prymak
Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewi…