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),
V.M. Traktyns'ka (Oles Honchar Dnipropetrovsk National University)


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.


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


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) doi:10.1007/BF01058514

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

Korneichuk N.P. Exact constants in approximation theory, Nauka, Moscow, 1987; 424 p. (in Russian)

Pinkus A., Strauss H. "$$$L_1$$$-approximation with Constraints", Trans. Amer. Math. Soc., 1990; 322(1): pp. 239-261. doi:10.1090/S0002-9947-1990-0986698-6

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

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




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