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Best constants for tensor products of Bernstein, Szász and Baskakov operators
Published online by Cambridge University Press: 17 April 2009
Abstract
We consider tensor product operators and discuss their best constants in preservation inequalities concerning the usual moduli of continuity. In a previous paper, we obtained lower and upper bounds on such constants, under fairly general assumptions on the operators. Here, we concentrate on the l∞-modulus of continuity and three celebrated families of operators. For the tensor product of k identical copies of the Bernstein operator Bn, we show that the best uniform constant coincides with the dimension k when k ≥ 3, while, in case k = 2, it lies in the interval [2, 5/2] but depends upon n. Similar results also hold when Bn is replaced by a univariate Szász or Baskakov operator. The three proofs follow the same pattern, a crucial ingredient being some special properties of the probability distributions involved in the mentioned operators, namely: the binomial, Poisson, and negative binomial distributions.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 211 - 220
- Copyright
- Copyright © Australian Mathematical Society 2000
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