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math.CA2019★ 1 cited
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…
math.CA2019
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…
math.CA2019
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\…