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Matematicheskie Zametki, 2015, Volume 98, Issue 4, Pages 511–529
DOI: https://doi.org/10.4213/mzm10640 (Mi mzm10640) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$

S. B. Vakarchuk

Alfred Nobel University Dnepropetrovsk
Full-text PDF (595 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm10640
Abstract: In the space $L_2$, we study a number of smoothness characteristics of functions; our study is based on the use of the generalized shift operator $\tau_h$. For the case in which $\tau$ is the Steklov operator $S$, we obtain exact constants in Jackson-type inequalities for some classes of $2\pi$-periodic functions. We also calculate the exact values of the $n$-widths of function classes defined by the smoothness characteristics under consideration.
Keywords: Jackson-type inequality, $n$-width of a function class, Steklov operator, smoothness characteristic, generalized shift operator $\tau_h$, Minkowski's inequality, majorant, trigonometric polynomial, Rolle's theorem.
Received: 14.12.2014
Revised: 26.03.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 4, Pages 572–588
DOI: https://doi.org/10.1134/S0001434615090254
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. B. Vakarchuk, “Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$”, Mat. Zametki, 98:4 (2015), 511–529; Math. Notes, 98:4 (2015), 572–588
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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