关于Bernstein多项式的绝对收敛性(英文)

On Absolute Convergence of Bernstein Polynomials

英文关键词:Bernstein polynomial  absolute convergence.

中文摘要:

      该文研究Ｂｅｒｎｓｔｅｉｎ多项式的绝对收敛性．证明了，对每个ｘ∈［０，１］，一个有界变差函数的Ｂｅｒｎｓｔｅｉｎ多项式序列是绝对｜Ｃ，１｜可和的，而且给出了Ｂｅｒｓｔｅｉｎ多项式序列的绝对｜Ｃ，１｜和式的余项的估计．

英文摘要:

      This note is devoted to the study of the absolute convergence of Bernstein polynomials. It is proved that for each x∈[0,1], the sequence of the Bernstein polynomials of a function of bounded variation is absolutely summable by |C,1| method. Moreover, the estimate of the remainders of the |C,1| sum of the sequence of the Bernstein polynomials is obtained.