On an Extremal Problem concerning Bernstein Operators

Gonska, 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 -