Bernsteinα-多项式对单调函数的保持性质

Properties preserved by Bernsteinα-polynomials for monotonic functions

研究了文献[1]中提出的一元Bernsteinα-多项式,给出其关于函数单调性的保持性质,并构造出单纯形上二元Bernsteinα-多项式,也给出类似于一元的结果.

In this paper, firstly, one-dimensional Bemstein α - polynomial which is introduced in the paper[ 1 ] is studied, and some properties related to monotonic functions are preserved by the polynomial. Then two-dimensional Bemstein α- polynomials on simplex are constructed, and the results similar to those of one-dimensional polynomial are obtained.