Xie, Lin Sen, Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials, Acta mathematica Sinica. English series (Print) , 21(5), 2005, pp. 1241-1248
We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth DitzianTotik modulus of smoothness r(f,t)where is an admissible stepweight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.