On Constants in Estimates of Approximations by Entire Functions of Exponential Type in Terms of Moduli of Continuity of Derivatives

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On Constants in Estimates of Approximations by Entire Functions of Exponential Type in Terms of Moduli of Continuity of Derivatives. / Babushkin, M. V.; Vinogradov, O. L.

In: Journal of Mathematical Sciences (United States), Vol. 261, No. 3, 07.03.2022, p. 353-365.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2621929042b548f9bfe5f4fd22586ce6,

title = "On Constants in Estimates of Approximations by Entire Functions of Exponential Type in Terms of Moduli of Continuity of Derivatives",

abstract = "We propose a new method for proving Jackson type inequalities for not necessarily periodic functions defined on the whole real line. In the inequalities under consideration, the best approximations by entire functions of exponential type are estimated in terms of the moduli of continuity of the derivatives of the approximated function. For some values of the parameters the obtained constants are less than the known ones. We construct linear approximation methods for realizing the obtained inequalities.",

author = "Babushkin, {M. V.} and Vinogradov, {O. L.}",

note = "Publisher Copyright: {\textcopyright} 2022, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = mar,

day = "7",

doi = "10.1007/s10958-022-05755-6",

language = "English",

volume = "261",

pages = "353--365",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - On Constants in Estimates of Approximations by Entire Functions of Exponential Type in Terms of Moduli of Continuity of Derivatives

AU - Babushkin, M. V.

AU - Vinogradov, O. L.

PY - 2022/3/7

Y1 - 2022/3/7

N2 - We propose a new method for proving Jackson type inequalities for not necessarily periodic functions defined on the whole real line. In the inequalities under consideration, the best approximations by entire functions of exponential type are estimated in terms of the moduli of continuity of the derivatives of the approximated function. For some values of the parameters the obtained constants are less than the known ones. We construct linear approximation methods for realizing the obtained inequalities.

AB - We propose a new method for proving Jackson type inequalities for not necessarily periodic functions defined on the whole real line. In the inequalities under consideration, the best approximations by entire functions of exponential type are estimated in terms of the moduli of continuity of the derivatives of the approximated function. For some values of the parameters the obtained constants are less than the known ones. We construct linear approximation methods for realizing the obtained inequalities.

UR - http://www.scopus.com/inward/record.url?scp=85125698728&partnerID=8YFLogxK

U2 - 10.1007/s10958-022-05755-6

DO - 10.1007/s10958-022-05755-6

M3 - Article

AN - SCOPUS:85125698728

VL - 261

SP - 353

EP - 365

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 101356395