Article ID Journal Published Year Pages File Type
9503310 Journal of Mathematical Analysis and Applications 2005 12 Pages PDF
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+k1−1/p is the best uniform constant for a single operator; the second one gives sufficient conditions in order that 1+k1−1/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.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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