Some negative results for the interpolation monotone approximation of functions having a fractional derivative
Тип публікації :
Стаття
Дата випуску :
2020
Автор(и) :
Petrova, T. O.
Chulakov, I. P.
Мова основного тексту :
Англійська
eKNUTSHIR URL :
Випуск :
3
ISSN :
1812-5409
Початкова сторінка :
122
Кінцева сторінка :
127
Цитування :
[APA 7] Petrova, T. O., & Chulakov, I. P. (2020). Some negative results for the interpolation monotone approximation of functions having a fractional derivative. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (3), 122–127. https://doi.org/10.17721/1812-5409.2020/3.14
[ДСТУ] Petrova T. O., Chulakov I. P. Some negative results for the interpolation monotone approximation of functions having a fractional derivative. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2020. no. 3. P. 122—127. DOI: 10.17721/1812-5409.2020/3.14 (date of access: 18.07.2026).
We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function $f ? W^r [0,1]$ by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function $f ? C^r [0,1] \cap \Delta^0$ where $\Delta^0$ is the set of positive functions on [0,1].Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider $r ? ?, r > 2$. In [8] is consider $r ? ?, r > 2$. It was proved that for monotone approximation estimates of the form (1) are fails for $r ? ?, r > 2$. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6]). In [5] is consider $r ? ?, r > 2$. In [6] is consider $r ? ?, r > 2$. It was proved that for convex approximation estimates of the form (1) are fails for $r ? ?, r > 2$. In this paper the question of approximation of function $f ? W^r \cap \Delta^1, r ? (3,4)$ by algebraic polynomial $p_n ? \Pi_n \cap \Delta^1$ is consider. The main result of the work generalize the result of work [8] for $r ? (3,4)$.Key words: approximation of function, Sobolev space, algebraic polynomial, monotone function, convex function.Pages of the article in the issue: 122 - 127Language of the article: Ukrainian
Файл(и) :![Ескіз]()
Вантажиться...
Формат :
Adobe PDF
Розмір :
657.88 KB
Контрольна сума :
(MD5):d21ad1ed10151fa427e855bc097389c0
Якщо не вказано інше, ця робота розповсюджується на умовах ліцензії Creative Commons Attribution 4.0 International