The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight for continuous functions with values in KB-space

M.Ye. Tkachenko (Oles Honchar Dnipro National University)
V.M. Traktynska (Oles Honchar Dnipro National University)

Abstract


We investigate the problem of uniqueness of the best non-symmetrical $$$L_1$$$-approximant with a weight for continuous functions on metric compact set $$$Q$$$ with values in strictly convex partially ordered KB-space $$$X$$$ by subspaces of space $$$C(Q, X)$$$ of continuous functions on $$$Q$$$ with values in $$$X$$$. We obtain the characterization of subspaces of uniqueness of the best $$$(\alpha, \beta)$$$-approximant in integral metric with a weight for functions of space $$$C(Q, X)$$$ in terms of classes of "test" functions.

Keywords


uniqueness of the best non-symmetric approximant with a weight; $$$(\alpha, \beta)$$$-approximation with a weight; integral metric; KB-space

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References


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Babenko V.F., Tkachenko M.Ye. "Problems of unicity of the best non-symmetric $$$L_1$$$-approximant of continuous functions with values in KB-spaces", Ukrainian Math. J., 2008; 60(7): pp. 867-878. (in Russian)

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Tkachenko M.Ye., Traktynska V.M. "Criterions for the best non-symmetric $$$L_p$$$- and $$$L_1$$$-approximant for the functions with values in KB-spaces with weight", Dnipr. Univ. Math. Bull., 2017; 22: pp. 97-102. (in Ukrainian)




DOI: https://dx.doi.org/10.15421/241907

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