# On an Extremal Problem concerning Bernstein Operators

Gonska, Heinz; Zhou, Ding-Xuan

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 2, page 137-150
- ISSN: 1310-6600

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topGonska, Heinz, and Zhou, Ding-Xuan. "On an Extremal Problem concerning Bernstein Operators." Serdica Mathematical Journal 21.2 (1995): 137-150. <http://eudml.org/doc/11663>.

@article{Gonska1995,

abstract = {* 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.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.},

author = {Gonska, Heinz, Zhou, Ding-Xuan},

journal = {Serdica Mathematical Journal},

keywords = {Bernstein Operators; Best Constant; Second Modulus of Smoothness; K-Functional; -functional; Bernstein operators; second modulus of smoothness},

language = {eng},

number = {2},

pages = {137-150},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On an Extremal Problem concerning Bernstein Operators},

url = {http://eudml.org/doc/11663},

volume = {21},

year = {1995},

}

TY - JOUR

AU - Gonska, Heinz

AU - Zhou, Ding-Xuan

TI - On an Extremal Problem concerning Bernstein Operators

JO - Serdica Mathematical Journal

PY - 1995

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 21

IS - 2

SP - 137

EP - 150

AB - * 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.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.

LA - eng

KW - Bernstein Operators; Best Constant; Second Modulus of Smoothness; K-Functional; -functional; Bernstein operators; second modulus of smoothness

UR - http://eudml.org/doc/11663

ER -

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