Abstract:
Two-sided estimates in terms of the best approximations by trigonometric polynomials are established for some functionals connected with approximation theory.
Key words and phrases:modulus of continuity, best approximation, Fejer and Jackson integrals, Fejer–Vallee Poussin and Jackson–Vallee Poussin integrals.
Citation:
M. V. Babushkin, V. V. Zhuk, “On two-sided estimates for some functionals in terms of the best approximations”, Analytical theory of numbers and theory of functions. Part 32, Zap. Nauchn. Sem. POMI, 449, POMI, St. Petersburg, 2016, 15–31; J. Math. Sci. (N. Y.), 225:6 (2017), 848–858
\Bibitem{BabZhu16}
\by M.~V.~Babushkin, V.~V.~Zhuk
\paper On two-sided estimates for some functionals in terms of the best approximations
\inbook Analytical theory of numbers and theory of functions. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 449
\pages 15--31
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6320}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3580129}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 225
\issue 6
\pages 848--858
\crossref{https://doi.org/10.1007/s10958-017-3501-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85027340328}
Linking options:
https://www.mathnet.ru/eng/znsl6320
https://www.mathnet.ru/eng/znsl/v449/p15
This publication is cited in the following 2 articles:
O. L. Vinogradov, “On constants in abstract inverse theorems of approximation theory”, St. Petersburg Math. J., 34:4 (2023), 573–589
O. L. Vinogradov, “ON THE CONSTANT IN THE ESTIMATE OF DEVIATION OF FEJÉR AVERAGES IN TERMS OF BEST APPROXIMATIONS”, J Math Sci, 266:4 (2022), 517