Conditions of unicity of the best non-symmetric $$$L_1$$$-approximant for continuous vector-valued functions by one-dimensional subspace

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 for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

Keywords


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

References


Babenko V.F., Tkachenko M.Ye. "Sufficient conditions of unicity of the best $$$L_1$$$-approximant for the functions with values in Banach space", Dnipr. Univ. Math. Bull., 2003; 8: pp. 19-25. (in Ukrainian)

Tkachenko M.Ye. "On unicity of the best approximant for vector-valued functions being continuous on metric compact", Dnipr. Univ. Math. Bull., 2001; pp. 121-127. (in Russian)

Tkachenko M.Ye. "Sufficient conditions of unicity of the best non-symmetric $$$L_1$$$-approximant for functions with values in KB-space", Dnipr. Univ. Math. Bull., 2006; 11: pp. 90-97. (in Ukrainian)

Tkachenko M.Ye., Traktyns'ka V.M. "Conditions of unicity of the best $$$L_1$$$-approximant for vector-valued functions by subspace of constant maps", Dnipr. Univ. Math. Bull., 2008; 13: pp. 144-148. (in Russian)

Tkachenko M.Ye., Traktyns'ka V.M. "Conditions of unicity of the best non-symmetric $$$L_1$$$-approximant for vector-valued functions by subspace of constant maps", Dnipr. Univ. Math. Bull., 2009; 14: pp. 133-139. (in Russian)

Tkachenko M.Ye., Traktyns'ka V.M. "Conditions of unicity of the best non-symmetric $$$L_1$$$-approximant for vector-valued functions by one-dimensional subspace", Dnipr. Univ. Math. Bull., 2011; 16: pp. 123-128. (in Russian)


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