On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$

On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$

Estimates above and estimates below have been obtained for Kolmogorov, linear and Bernshtein average $\nu$-widths on the classes of functions $W^r (\omega^w, \Psi)$, where $r \in \mathbb{N}$, $\omega^w(f)$ is the generalized characteristic of smoothness of a function $f \in L_2(\mathbb{R})$, $\Psi$...

Full description

Bibliographic Details
Main Authors: S.B. Vakarchuk, M.B. Vakarchuk
Format: Article
Language:English
Published: Oles Honchar Dnipro National University 2019-07-01
Series:Researches in Mathematics
Subjects:
generalized modulus of continuity
majorant
entire function
average $\nu$-width
Online Access:https://vestnmath.dnu.dp.ua/index.php/rim/article/view/109
id doaj-632e4b13b0bc48389a4669f0d3aac04d
record_format Article
spelling doaj-632e4b13b0bc48389a4669f0d3aac04d2020-11-25T03:43:03ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092019-07-01271142710.15421/241902On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$S.B. Vakarchuk0M.B. Vakarchuk1Alfred Nobel UniversityOles Honchar Dnipro National UniversityEstimates above and estimates below have been obtained for Kolmogorov, linear and Bernshtein average $\nu$-widths on the classes of functions $W^r (\omega^w, \Psi)$, where $r \in \mathbb{N}$, $\omega^w(f)$ is the generalized characteristic of smoothness of a function $f \in L_2(\mathbb{R})$, $\Psi$ is a majorant. Exact values of the enumerated extremal characteristics of approximation, following from the one condition on the majorant were obtained too.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/109generalized modulus of continuitymajorantentire functionaverage $\nu$-width
collection DOAJ
language English
format Article
sources DOAJ
author S.B. Vakarchuk
M.B. Vakarchuk
spellingShingle S.B. Vakarchuk
M.B. Vakarchuk
On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$
Researches in Mathematics
generalized modulus of continuity
majorant
entire function
average $\nu$-width
author_facet S.B. Vakarchuk
M.B. Vakarchuk
author_sort S.B. Vakarchuk
title On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$
title_short On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$
title_full On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$
title_fullStr On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$
title_full_unstemmed On generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $L_2(\mathbb{R})$
title_sort on generalized characteristics of smoothness of functions and on average $\nu$-widths in the space $l_2(\mathbb{r})$
publisher Oles Honchar Dnipro National University
series Researches in Mathematics
issn 2664-4991
2664-5009
publishDate 2019-07-01
description Estimates above and estimates below have been obtained for Kolmogorov, linear and Bernshtein average $\nu$-widths on the classes of functions $W^r (\omega^w, \Psi)$, where $r \in \mathbb{N}$, $\omega^w(f)$ is the generalized characteristic of smoothness of a function $f \in L_2(\mathbb{R})$, $\Psi$ is a majorant. Exact values of the enumerated extremal characteristics of approximation, following from the one condition on the majorant were obtained too.
topic generalized modulus of continuity
majorant
entire function
average $\nu$-width
url https://vestnmath.dnu.dp.ua/index.php/rim/article/view/109
work_keys_str_mv AT sbvakarchuk ongeneralizedcharacteristicsofsmoothnessoffunctionsandonaveragenuwidthsinthespacel2mathbbr
AT mbvakarchuk ongeneralizedcharacteristicsofsmoothnessoffunctionsandonaveragenuwidthsinthespacel2mathbbr
_version_ 1724521564250046464

Similar Items