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Modelirovanie i Analiz Informatsionnykh Sistem, 2015, Volume 22, Number 1, Pages 127–143
(Mi mais425)
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On the approximation of periodic functions in $L_2$ and the values of the widths of certain classes of functions
K. Tukhliev Khujand State University, Mavlonbekova, 1, Khujand, 735700, Tajikistan
Abstract:
The sharp Jackson–Stechkin inequalities are received, in which a special module of continuity $\widetilde{\Omega}_{m}(f; t)$ determined by Steklov's function is used instead the usual modulus of continuity of $m$th order $\omega_{m}(f; t)$. Such generalized modulus of continuity of $m$th order were introduced by V. A. Abilov and F. V. Abilova. The introduced modulus of continuity found their application in the theory of polynomial approximation in Hilbert space in the works by M. Sh. Shabozov and G. A. Yusupov, S. B. Vakarchuk and V. I. Zabutnaya and others.
While continuing and developing these direction for some classes of functions defined by modulus of continuity, the new values of $n$-widths in the Hilbert space $L_{2}$ were found.
Keywords:
best polynomial approximation, Steklov operator, modulus of continuity, generalized modulus of continuity, $n$-widths.
Received: 15.11.2013
Citation:
K. Tukhliev, “On the approximation of periodic functions in $L_2$ and the values of the widths of certain classes of functions”, Model. Anal. Inform. Sist., 22:1 (2015), 127–143
Linking options:
https://www.mathnet.ru/eng/mais425 https://www.mathnet.ru/eng/mais/v22/i1/p127
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Abstract page: | 216 | Full-text PDF : | 179 | References: | 30 |
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