Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634924 | Applied Mathematics and Computation | 2008 | 10 Pages |
Abstract
In this paper, the q-Bernstein polynomials Bn,q(fa;z) of the Cauchy kernel fa=1/(z-a),aâCâ§¹[0,1] are found explicitly and their properties are investigated. In particular, it is proved that if q>1, then polynomials Bn,q(fa;z) converge to fa uniformly on any compact set Kâ{z:|z|<|a|}. This result is sharp in the following sense: on any set with an accumulation point in {z:|z|>|a|}, the sequence {Bn,q(fa;z)} is not even uniformly bounded.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sofiya Ostrovska,