Abstract
We study the possibility of uniform approximation of continuous mappings of metric compact sets into metric spaces. Notions of “weak dimension” and “weak Kolmogorov width” are introduced to compare approximating properties of infinite-dimensional subspaces. For classes of mappings specified by the majorant of the modulus of continuity, we present bilateral estimates of “weak” widths that may coincide under certain conditions.
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References
N. P. Korneichuk,Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1987).
I. M. Kolodii and F. Hildebrand, “On some properties of the modulus of continuity,”Mat. Zametki,9, No. 5, 495–500 (1971).
L. Dantzer, B. Grünbaum, and V. Klee,Helly's Theorem and Its Relatives, American Mathematical Society, Providence, RI (1963).
V. I. Berdyshev, “Relationship between the Jackson inequality and one geometric problem,”Mat. Zametki,3, No. 3, 327–338 (1968).
S. A. Pichugov, “Young constant of the spaceL p ,”Mat. Zametki,43, No. 5, 604–614 (1988).
I. K. Daugavet,Introduction to the Theory of Approximation of Functions [in Russian], Leningrad University, Leningrad (1977).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1435–1448, November, 1994.
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Babenko, V.F., Pichugov, S.A. Approximation of continuous vector functions. Ukr Math J 46, 1585–1599 (1994). https://doi.org/10.1007/BF01058878
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DOI: https://doi.org/10.1007/BF01058878