Abstract
We investigate the problem of the best uniform approximation of a function continuous on a compact set. We generalize the principal results of this investigation to the problem of the best simultaneous uniform approximation of a family of functions continuous on a compact set.
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REFERENCES
S. I. Zukhovitskii, “On Chebyshev approximation of real functions,” Usp. Mat. Nauk, 11, Issue 2 (65), 125–159 (1956).
A. L. Garkavi, “On the Chebyshev center and convex hull of a set,” Usp. Mat. Nauk, 19, Issue 6 (120), 139–145 (1964).
E. G. Gol'shtein, Duality Theory in Mathematical Programming, and Its Applications [in Russian], Nauka, Moscow (1971).
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
Yu. V. Gnatyuk, “Moment problem with generalized moments from a polyhedron,” in: Nonlinear Boundary-Value Problems in Mathematical Physics and Their Applications [in Ukrainian], Part 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1996), pp. 25–27.
P. J. Laurent, Approximation and Optimization [Russian translation], Mir, Moscow (1975).
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Gnatyuk, Y.V. Best Uniform Approximation of a Family of Functions Continuous on a Compact Set. Ukrainian Mathematical Journal 54, 1912–1919 (2002). https://doi.org/10.1023/A:1024056827744
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DOI: https://doi.org/10.1023/A:1024056827744