Аннотация:
Using one-sided Steklov means, we introduce a new modulus of smoothness in weighted Lorentz spaces. The direct and inverse approximation theorem for this modulus of smoothness are proved. Also, we estimate the rate of approximation by the Borel and Euler means in weighted Lorentz spaces.
Ключевые слова:
weighted Lorentz spaces, direct and inverse approximation theorems, Borel means, Euler means.
Supported by the Ministry of science and education of the Russian Federation in the framework of the basic part of the scientific research state task, project FSRR-2020-0006.
Поступила в редакцию: 17.08.2020 Исправленный вариант: 30.11.2020 Принята в печать: 09.12.2020
Образец цитирования:
S. S. Volosivets, “Modified modulus of smoothness and approximation in weighted Lorentz spaces by Borel and Euler means”, Пробл. анал. Issues Anal., 10(28):1 (2021), 87–100
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\by S.~S.~Volosivets
\paper Modified modulus of smoothness and approximation in weighted Lorentz spaces by Borel and Euler means
\jour Пробл. анал. Issues Anal.
\yr 2021
\vol 10(28)
\issue 1
\pages 87--100
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\crossref{https://doi.org/10.15393/j3.art.2021.8950}
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https://www.mathnet.ru/rus/pa318
https://www.mathnet.ru/rus/pa/v28/i1/p87
Эта публикация цитируется в следующих 4 статьяx:
S. Jafarov, “Approximation by Nörlund type means in the grand Lebesgue spaces with variable exponent”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 34:1 (2024), 19–32
Sadulla Jafarov, “On approximation properties of functions by means of Fourier and Faber series in weighted Lebesgue spaces with variable exponent”, Mathematica Moravica, 27:1 (2023), 97
С. С. Волосивец, “Функционалы реализации и описание модуля гладкости в пространствах Лебега с переменным показателем”, Изв. вузов. Матем., 2022, № 6, 13–25; S. S. Volosivets, “Realization functionals and description of a modulus of smoothness in variable exponent Lebesgue spaces”, Russian Math. (Iz. VUZ), 66:6 (2022), 8–19
S. S. Volosivets, “Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces”, Пробл. анал. Issues Anal., 11(29):2 (2022), 106–118
Цитирование в формате AMSBIB
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