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

M.Ye. Tkachenko; V.M. Traktyns'ka

doi:10.15421/241218

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), 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 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

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References

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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", Res. Math., 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", Res. Math., 2011; 16: pp. 123-128. (in Russian)