On approximation of continuous functions by piecewise-constant ones in integral metrics

O.V. Chernytska (Dnipropetrovsk State University)

Abstract


We obtain upper bound of the best approximation of the classes $$$H^{\omega} [a, b]$$$ by piecewise-constant functions over uniform split in metrics of $$$L_{\varphi}[a, b]$$$ spaces, which are generated by continuous non-decreasing functions $$$\varphi$$$ that are equal to zero in zero. We study the classes of functions $$$\varphi$$$, for which the obtained bound is exact for all convex moduli of continuity.

References


Korneichuk N.P. "On one extremal problem", Questions of funct. approx. theory, 1980. (in Russian)

Korneichuk N.P. Splines in approximation theory, Nauka, 1984. (in Russian)

Korneichuk N.P. Exact constants in approximation theory, Nauka, 1987. (in Russian)

Natanson I.P. Theory of real variable functions, Nauka, 1974. (in Russian)




DOI: https://doi.org/10.15421/249819

  

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Copyright (c) 1998 O.V. Chernytska

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU