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On restricted derivative approximation. (English) Zbl 0697.41002
Summary: We show that the condition that f be 2k continuously differentiable is not necessary in order to guarantee the same order of approximation for both the restricted and the nonrestricted cases. Thus, we strengthen a result of J. A. Roulier [J. Approximation theory 17, 344-347 (1976; Zbl 0362.41012)].
MSC:
41A10 Approximation by polynomials
41A50 Best approximation, Chebyshev systems
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References:
[1] Roulier, J.A. , Best Approximation to Functions with Restricted derivate , J. Approximation Theory 17 (1976), 344-347. · Zbl 0362.41012 · doi:10.1016/0021-9045(76)90078-2
[2] Feinerman, R.P. and Newman, D.J. , ” Polynomial Approximation ”, Williams and Wilkins, Baltimore 1974. · Zbl 0309.41006
[3] Leviatan, D. , The behavior of the derivatives of the algebraic polynomials of best approximation , J. Approximation Theory 35 (1982), 169-176. · Zbl 0489.41016 · doi:10.1016/0021-9045(82)90034-X
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