AN ESTIMATION ABOUT THE APPROXIMATION BY BERNSTEIN POLYNOMIAL OF DISPERSIVENESS FOR A CONTINUOUS FUNCTION
Peng Shao · Advances in Mathematics · 1958
Let{r_n}be a sequence integers such that 0=r_or_1r_2…r_n…, rn→∞. For a continuous function f(x)defined on 0≤x≤1, we write the so-called Berstein Polynomial of dispersiveness with degree r_n. Professor L.C. Hsu and Mr.T. S. Wang had obtained the following result: uniform on δ≤x≤l-δfor every small fixed δ0. The object of this note is to prove the following: If r_n-r_(n_1)=O(r_n~a),(0≤a1/2), we have Theorem. where e0 is any, positive constant, and At last, the author have made a conjecture in the following: