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Hausdorff diameter of a nonsymmetric class of vector functions

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Abstract

In the space of parametrically determined m-dimensional curves with the Hausdorff metric, we find the diameter of a class of curves whose coordinate functions satisfy the Lipschitz condition on some segment and take fixed values at its endpoints. We obtain the dependence of relations determining the value of the diameter on the evenness of m.

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References

  1. BI. Sendov, Hausdorff Approximations, Bulgarian Academy of Sciences, Sofia (1979).

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  2. N. P. Korneichuk, “On optimal coding vector functions,” Ukr. Mat. Zh., 40, No. 6, 737–744 (1988).

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  3. A. A. Polovina, “Optimal coding of a class of vector functions,” Ukr. Mat. Zh., 49, No. 12, 1638–1645 (1997).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. A. Polovina

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  1. A. A. Polovina
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1570–1573, November, 1998.

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Polovina, A.A. Hausdorff diameter of a nonsymmetric class of vector functions. Ukr Math J 50, 1792–1795 (1998). https://doi.org/10.1007/BF02524488

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  • DOI: https://doi.org/10.1007/BF02524488

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