On uniqueness of the best non-symmetric approximant for vector-valued functions in $$$L_1$$$ metric

M.Ye. Gorbenko (Dnipropetrovsk State University), https://orcid.org/0000-0002-9242-194X

Abstract


We describe classes of test functions that characterize the space of uniqueness of the best non-symmetric $$$L_1$$$-approximant for vector-valued functions that are continuous in the interval.

References


Babenko V.F., Glushko V.N. "On uniqueness of the best approximant in metric of $$$L_1$$$ space", Ukrainian Math. J., 1994; 46(5): pp. 475-483. (in Russian) doi:10.1007/BF01058514

Babenko V.F., Zaiats I.F. "Non-symmetric $$$L_1$$$-approximations of vector-valued functions", Approx. of functions and summ. of series, Dnipropetrovsk, 1991. (in Russian)

Glushko V.N. Conditions of uuniqueness of the best one-side $$$L_1$$$-approximant, Diss. cand. phys.-math. sc., Dnipropetrovsk, 1992. (in Russian)

Strauss H. "Uniqueness in $$$L_1$$$-approximation", Math. Zeitschr., 1981; 176: pp. 63-74. (in German) doi:10.1007/BF01258905




DOI: https://doi.org/10.15421/249805

  

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Copyright (c) 1998 M.Ye. Gorbenko

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ISSN (Online): 2664-5009
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