Geodesic
On an Extremal Problem concerning Bernstein Operators
Serdica Mathematical Journal, Tome 21 (1995) no. 2, pp. 137-150

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The best constant problem for Bernstein operators with respect to the second modulus of smoothness is considered. We show that for any 1/2 ≤ a 1, there is an N(a) ∈ N such that for n ≥ N(a), 1−a≤k, n≤a, sup | Bn (f, k/n) − f(k/n) | ≤ cω2(f, 1/√n), where c is a constant,0 c 1.
Keywords: Bernstein Operators, Best Constant, Second Modulus of Smoothness, K-Functional 
Gonska, Heinz; Zhou, Ding-Xuan. On an Extremal Problem concerning Bernstein Operators. Serdica Mathematical Journal, Tome 21 (1995) no. 2, pp. 137-150. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_2_a3/
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     title = {On an {Extremal} {Problem} concerning {Bernstein} {Operators}},
     journal = {Serdica Mathematical Journal},
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     year = {1995},
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     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_1995_21_2_a3/}
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