Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials

Lin Sen Xie
October 2005
Acta Mathematica Sinica;Oct2005, Vol. 21 Issue 5, p1241
Academic Journal
We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian–Totik modulus of smoothness $$ \omega ^{r}_{\Phi } (f,t) $$where Φ is an admissible step–weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.


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