33 citations · 40 across the 12 of their papers we have counts for
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math.CA2014
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…
math.CA2014
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…
math.NA2014★ 3 cited
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…