多變數Bernstein多項式的一些性質
碩士 === 輔仁大學 === 數學系研究所 === 98 === It is known that multivariate Bernstein polynomials do not preserve convexity althrough it is true for univariate case. The problem could be fixed if the concept of convexity were gener- alized to axial convexity or polyhedral convexity. We introduce these two notio...
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| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2010
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| Online Access: | http://ndltd.ncl.edu.tw/handle/23832283059096068638 |
| Summary: | 碩士 === 輔仁大學 === 數學系研究所 === 98 === It is known that multivariate Bernstein polynomials do not
preserve convexity althrough it is true for univariate case. The
problem could be fixed if the concept of convexity were gener-
alized to axial convexity or polyhedral convexity. We introduce
these two notions and show that multivariate Bernstein poly-
nomials preserve each of them.
On the other hand, multivariate Bernstein operators possess
monotonicity if they act on convex or axially convex functions.
A simple proof will be given using probabilistic methods. In
addition, a large class of multivariate Bernstein-type operators
are also monotonic. Examples are given to illustrate the fact.
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