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Title: On an Extremal Problem concerning Bernstein Operators
Authors: Gonska, Heinz
Zhou, Ding-Xuan
Keywords: Bernstein Operators
Best Constant
Second Modulus of Smoothness
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 2, (1995), 137p-150p
Abstract: 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.
Description: * The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 2

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