Pointwise Approximation For The Iterated Boolean Sums Of Bernstein Operators

The aim of this paper is to discuss the pointwise approximation properties forthe iterated Boolean sums (?)rBn=sum from l=1 to r(?)(-1)l-1Bnl of Bernstein operator Bn．Firstly we give the expression and the upper estimate of(I-Bn)r((·-x)j,x)andBnl((·-x)2r,x)(l≥1)．Then with the help of moduli of smoothnessω(?)λ2r(f,t)we ob-tain direct and inverse theorems on pointwise approximation for operator (?)rBn(f,x)when 1-1/r≤λ≤1,r∈N．From these results we find that (?)rBn(f,x)can accel-erate convergence．...