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Mat. Zametki, 2015, Volume 98, Issue 4, Pages 511–529 (Mi mz10640)  

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

S. B. Vakarchuk

Alfred Nobel University Dnepropetrovsk

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.

DOI: https://doi.org/10.4213/mzm10640

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English version:
Mathematical Notes, 2015, 98:4, 572–588

Bibliographic databases:

UDC: 517.5
Received: 14.12.2014
Revised: 26.03.2015

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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