ONE-SIDED WIDTHS OF CLASSES OF SMOOTH FUNCTIONS

Yurii N. Subbotin     (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences; Institute of Mathematics and Computer Science, Ural Federal University, Russian Federation)

Abstract


One-sided widths of the classes of functions Wpr[0,1] in the metric Lq [0,1], 1≤ p, q ≤ ∞, r ≥ 1 are studied. Such widths are defined similarly to Kolmogorov widths with additional constraints on the approximating functions.

Keywords


One-sided widths; Exact orders; Classes of smooth functions

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References


Kolmogoroff A. Über die beste Annäherung von Funktionen einer geqebenen Functionenklasse // Ann. Math. 1936. Vol. 37. P. 107–111.

Korneichuk N. P., Ligun A. A. and Doronin V. G. Approximation With Constraints. Kiev: Naukova Dumka. 1982. 250 p. [in Russian].

Kashin B. S. Diameters of some finite-dimensional sets and classes of smooth functions // Izv. Math. 1977. Vol. 11, no. 2. P. 334–351.

Birkhoff G., Schultz M. H. and Varga R. S. Piecewise Hermite interpolation in one and two variables with application to partial differential equations // Numer. Math. 1968. Vol. 11. P. 232–256.




DOI: http://dx.doi.org/10.15826/umj.2015.1.008

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