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

M.Ye. Tkachenko; V.M. Traktynska

doi:10.15421/241118

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

M.Ye. Tkachenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-9242-194X
V.M. Traktynska (Oles Honchar Dnipropetrovsk National University)

Abstract

The conditions of the unicity of the best nonsymmetric $$$L_1$$$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

Keywords

the unicity of the best nonsymmetric $$$L_1$$$-approximant; vector-valued functions; one-dimensional subspace

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References

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Gorbenko M.Ye. "On unicity of the best nonsymmetric approximant for vector-valued functions in $$$L_1$$$ metric", Res. Math., 1998; 3: pp. 33-41. (in Russian)

Tkachenko M.Ye. "Sufficient conditions of unicity of the best non-symmetric $$$L_1$$$-approximant for functions with values in KB-space", Res. Math., 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", Res. Math., 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", Res. Math., 2009; 14: pp. 133-139. (in Russian)