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Approximation of continuous vector functions

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Abstract

We study the possibility of uniform approximation of continuous mappings of metric compact sets into metric spaces. Notions of “weak dimension” and “weak Kolmogorov width” are introduced to compare approximating properties of infinite-dimensional subspaces. For classes of mappings specified by the majorant of the modulus of continuity, we present bilateral estimates of “weak” widths that may coincide under certain conditions.

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Authors and Affiliations

  1. Dnepropetrovsk University, Dnepropetrovsk

    V. F. Babenko & S. A. Pichugov

Authors
  1. V. F. Babenko
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  2. S. A. Pichugov
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1435–1448, November, 1994.

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Babenko, V.F., Pichugov, S.A. Approximation of continuous vector functions. Ukr Math J 46, 1585–1599 (1994). https://doi.org/10.1007/BF01058878

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  • DOI: https://doi.org/10.1007/BF01058878

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