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)

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)


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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557