We give an interesting generalization of the Bernstein polynomials. We find sufficient and necessary conditions for uniform convergence by the new polynomials, and we generalize the Bernstein theorem.
A Bernstein TypeLpInequality for a Certain Class of Polynomials
β Scribed by Robert Gardner; Amy Weems
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 115 KB
- Volume
- 219
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
We examine how many of the Bernstein basis functions \(x^{k}(1-x)^{n-k}, k=\) \(0, \ldots, n\), can be omitted such that linear combinations of the remaining polynomials are still dense in the space of continuous functions. Co 1994 Academic Press. Inc.
Goodman has recently studied certain variation diminishing properties of Bernstein polynomials on triangles. Introducing analogous definitions for the variation of a trivariate function, we study in the present paper corresponding results for the Bernstein polynomials defined on a tetrahedron. We ha