The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight by $$$A_{\alpha ,\beta }$$$-subspace

M.Ye. Tkachenko; V.O. Traktynskyi

doi:10.15421/242005

The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight by $$$A_{\alpha ,\beta }$$$-subspace

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

Abstract

The questions of the uniqueness of the best non-symmetric $$$L_1$$$-approximant with weight in the finite dimensional subspace and the connection of such tasks with $$$A_{\alpha ,\beta }$$$-subspaces were considered in this article. This result generalizes the known result of Kroo on the case of non-symmetric approximation.

Keywords

$$$(\alpha ,\beta)$$$-approximation; KB-space; $$$L_1$$$-norm; weight; continuous functions

MSC 2020

41A52; 41A65; 46B40

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References

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Tkachenko M.Ye., Traktynska V.M. "The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight for continuous functions with values in KB-space", Res. Math., 2019; 27(1): pp. 67-74. doi:10.15421/241907

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