Bernstein Operators Best Constant Second Modulus of Smoothness K-Functional
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 21, No 2, (1995), 137p-150p
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.
* 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.