Shevchuk, I. A. 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? Reviewer: D.Leviatan (Edmonton) Cited in 1 Document MSC: 41A10 Approximation by polynomials 41A25 Rate of convergence, degree of approximation Citations:Zbl 0060.168; Zbl 0042.071; Zbl 0085.280; Zbl 0083.289; Zbl 0138.044 PDFBibTeX XMLCite \textit{I. A. Shevchuk}, Sov. Math., Dokl. 40, No. 2, 349--354 (1990; Zbl 0719.41011); translation from Dokl. Akad. Nauk SSSR 308, No. 3, 537--541 (1989)