Zobrazeno 1 - 10
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pro vyhledávání: '"Shevchuk, I ."'
Autor:
Leviatan, D., Shevchuk, I. O.
We give here the final results about the validity of Jackson-type estimates in comonotone approximation of $2\pi$-periodic functions by trigonometric polynomials. For coconvex and the so called co-$q$-monotone, $q>2$, approximations, everything is kn
Externí odkaz:
http://arxiv.org/abs/2402.06103
This paper deals with approximation of smooth convex functions $f$ on an interval by convex algebraic polynomials which interpolate $f$ at the endpoints of this interval. We call such estimates "interpolatory". One important corollary of our main the
Externí odkaz:
http://arxiv.org/abs/2001.03769
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 turns out that, in certain cases, these degrees are the same. The main pu
Externí odkaz:
http://arxiv.org/abs/1901.03911
We give an estimate of the general divided differences $[x_0,\dots,x_m;f]$, where some of the $x_i$'s are allowed to coalesce (in which case, $f$ is assumed to be sufficiently smooth). This estimate is then applied to significantly strengthen Whitney
Externí odkaz:
http://arxiv.org/abs/1901.03908
We discuss some properties of the moduli of smoothness with Jacobi weights that we have recently introduced and that are defined as \[ \omega_{k,r}^\varphi(f^{(r)},t)_{\alpha,\beta,p} :=\sup_{0\leq h\leq t} \left\| {\mathcal{W}}_{kh}^{r/2+\alpha,r/2+
Externí odkaz:
http://arxiv.org/abs/1901.03907
Given a nondecreasing function $f$ on $[-1,1]$, we investigate how well it can be approximated by nondecreasing algebraic polynomials that interpolate it at $\pm 1$. We establish pointwise estimates of the approximation error by such polynomials that
Externí odkaz:
http://arxiv.org/abs/1711.07083
Akademický článek
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Akademický článek
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Publikováno v:
Journal of Approximation Theory 210 (2016) 1-22
For each $q\in{\mathbb{N}}_0$, we construct positive linear polynomial approximation operators $M_n$ that simultaneously preserve $k$-monotonicity for all $0\leq k\leq q$ and yield the estimate \[ |f(x)-M_n(f, x)| \leq c \omega_2^{\varphi^\lambda} \l
Externí odkaz:
http://arxiv.org/abs/1602.07313
Autor:
Leviatan, D.1 (AUTHOR) leviatan@tauex.tau.ac.il, Shevchuk, I. A.2 (AUTHOR)
Publikováno v:
Constructive Approximation. Apr2023, Vol. 57 Issue 2, p695-726. 32p.
