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pro vyhledávání: '"Shevchuk, Igor"'
It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur--Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings bet
Externí odkaz:
http://arxiv.org/abs/2209.01406
Autor:
Shevchuk, Igor V.
Publikováno v:
International Journal of Numerical Methods for Heat & Fluid Flow, 2023, Vol. 33, Issue 11, pp. 3770-3800.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/HFF-06-2023-0318
We establish best possible pointwise (up to a constant multiple) estimates for approximation, on a finite interval, by polynomials that satisfy finitely many (Hermite) interpolation conditions, and show that these estimates cannot be improved. In par
Externí odkaz:
http://arxiv.org/abs/2006.03126
We say that a function $f\in C[a,b]$ is $q$-monotone, $q\ge3$, if $f\in C^{q-2}(a,b)$ and $f^{(q-2)}$ is convex in $(a,b)$. Let $f$ be continuous and $2\pi$-periodic, and change its $q$-monotonicity finitely many times in $[-\pi,\pi]$. We are interes
Externí odkaz:
http://arxiv.org/abs/2004.03724
Publikováno v:
In Thermal Science and Engineering Progress 1 December 2023 46
Akademický článek
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Autor:
Shevchuk, Igor V.
Publikováno v:
International Journal of Numerical Methods for Heat & Fluid Flow, 2022, Vol. 33, Issue 1, pp. 204-225.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/HFF-03-2022-0168
In this paper, among other things, we show that, given $r\in N$, there is a constant $c=c(r)$ such that if $f\in C^r[-1,1]$ is convex, then there is a number ${\mathcal N}={\mathcal N}(f,r)$, depending on $f$ and $r$, such that for $n\ge{\mathcal N}$
Externí odkaz:
http://arxiv.org/abs/1811.01087