I. Shevchuk

activity

20112022

most citedUniform and Pointwise Shape Preserving Approximation by Algebraic Polynomials

33 citations · 35 across the 11 of their papers we have counts for

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Showing 2014Show all

2 papers · 1 filter

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 $f \in L_{p} [- 1, 1] \cap C^{r - 1} (- 1, 1)$ , $1 \leq p \leq \infty$ , $r \geq 1$ , that have an $(r - 1)$ st locally absolutely continuous derivative…