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)


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.


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

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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.

Strauss H. "Unicity in $$$L_1$$$-approximation", Math. Zeitschr., 1981; 176: pp. 63-74. (in German) doi:10.1007/BF01258905

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) doi:10.1007/s11253-008-0109-5

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

Tkachenko M.Ye., Traktyns'ka V.M. "Criterions for the best non-symmetric $$$L_p$$$- and $$$L_1$$$-approximant for the functions with values in KB-spaces with weight", Res. Math., 2017; 22: pp. 97-102. (in Ukrainian) doi:10.15421/241712




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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991