Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503310 | Journal of Mathematical Analysis and Applications | 2005 | 12 Pages |
Abstract
For the tensor product of k copies of the same one-dimensional Bernstein-type operator L, we consider the problem of finding the best constant in preservation of the usual modulus of continuity for the lp-norm on Rk. Two main results are obtained: the first one gives both necessary and sufficient conditions in order that 1+k1â1/p is the best uniform constant for a single operator; the second one gives sufficient conditions in order that 1+k1â1/p is the best uniform constant for a family of operators. The general results are applied to several classical families of operators usually considered in approximation theory. Throughout the paper, probabilistic concepts and methods play an important role.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jesús de la Cal, Javier Cárcamo,