Criterions for the best non-symmetric $$$L_p$$$- and $$$L_1$$$-approximant for the functions with values in KB-spaces with weight

M.Ye. Tkachenko (Oles Honchar Dnipropetrovsk National University)
V.M. Traktyns'ka (Oles Honchar Dnipropetrovsk National University)

Abstract


The questions of the characterization of the best non-symmetric $$$L_p$$$ and $$$L_1$$$-approximant for the functions with values in KB-space with a weight were considered. The criterions of the best non-symmetric approximant for the specified functions in metrics of the spaces $$$L_p$$$ and $$$L_1$$$ with a weight is obtained.

Keywords


non-symmetric norms; the functions with values in KB-space; the best non-symmetric approximant with a weight

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.

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

Rozema E. "Almost Chebyshev subspaces of $$$L_1(\mu, E)$$$", Pacif. J. Math, 1974; 53: pp. 585-604.

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)

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

Tkachenko M.Ye., Traktyns'ka V.M., Shkuratyuk K.O. "Criterion of the best non-symmetric $$$L_1$$$-approximant of continuous functions with values in KB-spaces", Proc. of International Conf. "Spring Scientific Readings, Part 1", Kyiv, 2016; pp. 31-36. (in Ukrainian)


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ISSN (Online): 2518-7996
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