Conditions of unicity of the best non-symmetric $$$L_1$$$-approximant

Yu.S. Zagorul'ko (Oles Honchar Dnipropetrovsk National University)
M.Ye. Tkachenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-9242-194X
V.M. Traktyns'ka (Oles Honchar Dnipropetrovsk National University)

Abstract


The necessary and sufficient conditions of the unicity of the best $$$(\overline{\alpha},\overline{\beta})$$$-approximant with coefficient constraints for the continuous vector-valued functions on a metric compact are obtained.

Keywords


the unicity of the best non-symmetric approximant; vector-valued functions; one-dimensional subspace

References


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

Gorbenko M.Ye. "On unicity of the best $$$L_1$$$-approximant with coefficient constraints", Dnipr. Univ. Math. Bull., 2000; 5: pp. 47-55. (in Russian)

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

Pinkus A., Strauss H. "$$$L_1$$$-approximation with Constraints", Trans. Amer. Math. Soc., 1990; 322(1): pp. 239-261.

Strauss H. "Unicity in $$$L_1$$$-approximation", Math. Zeitschr., 1981; pp. 63-74. (in German)

Tkachenko M.Ye. "On unicity of the best $$$L_1$$$-approximant with coefficient constraints for vector-valued functions", Dnipr. Univ. Math. Bull., 2002; 7: pp. 92-102. (in Russian)




DOI: https://dx.doi.org/10.15421/241312

  

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Copyright (c) 2013 Yu.S. Zagorul'ko, M.Ye. Tkachenko, V.M. Traktyns'ka

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