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On coapproximation of monotone functions. (English. Russian original) Zbl 0719.41011

Sov. Math., Dokl. 40, No. 2, 349-354 (1990); translation from Dokl. Akad. Nauk SSSR 308, No. 3, 537-541 (1989).
This article deals with following question: Are the direct theorems of S. M. Nikol’skij [Izv. Akad. Nauk SSSR Ser. Math. 10, 295-322 (1946; Zbl 0060.168)], A. F. Timan [Dokl. Akad. Nauk SSSR, N. Ser. 78, 17-20 (1951; Zbl 0042.071)], V. K. Dzyadyk [ibid. 121, 403-406 (1958; Zbl 0085.280)], G. Freud [Math. Ann. 137, 17-25 (1959; Zbl 0083.289)], and Yu. A. Brudnyĭ [Dokl. Akad. Nauk SSSR 148, 1237- 1240 (1963; Zbl 0138.044)] also true if a function monotone on \(I:=[- 1,1]\) is approximated by a polynomial monotone on I?

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
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