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Contemporary Mathematics. Fundamental Directions, 2007, Volume 25, Pages 149–164 (Mi cmfd112)  
On the Connection Between the Best Approximation by Algebraic Polynomials and the Modulus of Smoothness of Order $r$

M. K. Potapova, F. M. Berishab

a M. V. Lomonosov Moscow State University
b University of Prishtina, Serbia
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Abstract: We introduce a family of asymmetric generalized translations. In terms of these operators we define generalized miduli of smoothness for which the direct and inverse theorems of approximation theory are proved.
English version:
Journal of Mathematical Sciences, 2008, Volume 155, Issue 1, Pages 153–169
DOI: https://doi.org/10.1007/s10958-008-9217-x
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: M. K. Potapov, F. M. Berisha, “On the Connection Between the Best Approximation by Algebraic Polynomials and the Modulus of Smoothness of Order $r$”, Theory of functions, CMFD, 25, PFUR, M., 2007, 149–164; Journal of Mathematical Sciences, 155:1 (2008), 153–169
Citation in format AMSBIB
\Bibitem{PotBer07}
\by M.~K.~Potapov, F.~M.~Berisha
\paper On the Connection Between the Best Approximation by Algebraic Polynomials and the Modulus of Smoothness of Order~$r$
\inbook Theory of functions
\serial CMFD
\yr 2007
\vol 25
\pages 149--164
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd112}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2342544}
\zmath{https://zbmath.org/?q=an:1178.41014}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 155
\issue 1
\pages 153--169
\crossref{https://doi.org/10.1007/s10958-008-9217-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-55849107795}
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