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

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References


Kroo A. "A general approach to the study of Chebyshev subspaces in $$$L_1$$$-approximation of continuous functions", J. Approx. Theory, 1987; 51: pp. 98-111. doi:10.1016/0021-9045(87)90024-4

Pinkus A. $$$L_1$$$-Approximation, Cambridge Univ. Press, 1989; 239 p.

Strauβ H. "Eindeutigkeit in der $$$L_1$$$-approximation", Math. Zeitschr., 1981; pp. 63-74. (in German)

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

Vulikh B.Z. Introduction to the theory of semi-ordered spaces, Moscow, Fizmatgiz, 1961; 407 p. (in Russian)




DOI: https://dx.doi.org/10.15421/242005

  

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