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This article is cited in 7 scientific papers (total in 7 papers)
Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$
M. Sh. Shabozova, G. A. Yusupovb
a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe, Tajikistan
b Tajik National University, Dushanbe, Tajikistan
Abstract:
We find the exact values of the $n$-widths for the classes of periodic differentiable functions in $L_2[0,2\pi]$, satisfying the constraint
$$
\int_0^ht\widetilde\Omega_m^{1/m}(f^{(r)};t) dt\le\Phi(h),
$$
where $h>0$, $m\in\mathbb N$, $r\in\mathbb Z_+$, $\widetilde\Omega_m^{1/m}(f^{(r)};t)$ is the generalized $m$th order continuity modulus of the derivative $f^{(r)}\in L_2[0,2\pi]$, while $\Phi(t)$ is an arbitrary increasing function such that $\Phi(0)=0$.
Keywords:
space of square integrable functions, best approximation, extremal characteristic, generalized continuity modulus, width.
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English version:
Siberian Mathematical Journal, 2011, 52:6, 1124–1136
Bibliographic databases:
  
UDC:
517.5
Received: 11.01.2011
Revised: 10.05.2011
Citation:
M. Sh. Shabozov, G. A. Yusupov, “Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$”, Sibirsk. Mat. Zh., 52:6 (2011), 1414–1427; Siberian Math. J., 52:6 (2011), 1124–1136
Citation in format AMSBIB
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\pages 1414--1427
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\vol 52
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\pages 1124--1136
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http://mi.mathnet.ru/eng/smj2284 http://mi.mathnet.ru/eng/smj/v52/i6/p1414
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K. Tukhliev, “O priblizhenii periodicheskikh funktsii v $L_2$ i znacheniyakh poperechnikov nekotorykh klassov funktsii”, Model. i analiz inform. sistem, 22:1 (2015), 127–143
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S. B. Vakarchuk, “Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$”, Math. Notes, 98:4 (2015), 572–588
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S. B. Vakarchuk, V. I. Zabutnaya, “Inequalities between Best Polynomial Approximations and Some Smoothness Characteristics in the Space $L_2$ and Widths of Classes of Functions”, Math. Notes, 99:2 (2016), 222–242
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K. Tukhliev, “Nailuchshie priblizheniya i poperechniki nekotorykh klassov svertok v $L_{2}$”, Tr. IMM UrO RAN, 22, no. 4, 2016, 284–294
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S. B. Vakarchuk, “Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths for the classes of $(\psi, \beta)$-differentiable functions in $L_2$. I”, Ukr. Math. J., 68:6 (2016), 823–848
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Vakarchuk S.B., “on the Estimates of Widths of the Classes of Functions Defined By the Generalized Moduli of Continuity and Majorants in the Weighted Space l-2,l-X(0,1)”, Ukr. Math. J., 71:2 (2019), 202–214
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Babenko V.F., Konareva S.V., “Jackson-Stechkin-Type Inequalities For the Approximation of Elements of Hilbert Spaces”, Ukr. Math. J., 70:9 (2019), 1331–1344
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