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  • 1 ИМ. Я. КУПАЛЫ ГРОДНЕНСКИЙ ГОС УДАРСТВЕННЫЙ УНИВЕР СИТЕТ УЛ. ОЖЕ ШКО 22 230 023 ГРОДНО СССР
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The paper deals with the order of best rational approximation of some classes of functions, depending on their differentiability properties. Improvements and generalizations of some results by P. P. Petrushev, V. A. Popov and the author are obtained. The proofs are based on the author's direct rational approximation theorems received recently. One of the results reads as follows. LetRn(f,Lp) denote the value of the best approximation of a functionf inLp,f∈Lp [0,1], by rational fractions of degree not exceedingn, n≧1. Suppose that 0<p≦∞,s∈NU{0}, andp≠∞ fors=0. Iff is thes-th primitive of some function of bounded variation on [0,1], then
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{n = 1}^\infty {\frac{1}{n}(n^{s + 1} R_n (f,L_p ))^2< \infty }$$ \end{document}
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  • Impact Factor (2019): 0.527
  • Scimago Journal Rank (2019): 0.384
  • SJR Hirsch-Index (2019): 15
  • SJR Quartile Score (2019): Q3 Analysis
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.702
  • Scimago Journal Rank (2018): 0.47
  • SJR Hirsch-Index (2018): 14
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Analysis Mathematica
Language English
Size B5
Year of
Foundation
1975
Volumes
per Year
1
Issues
per Year
4
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)