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Pointwise weighted approximation by Bernstein operators
Authors:Shunsheng Guo  Hongzhi Tong  Gengsheng Zhang
Affiliation:(1) Department of Mathematics, Hebei Normal University, Shijiazhuang, 050016, P. R. China
Abstract:We consider the pointwise weighted approximation by Bernstein operators. The related weight functions are Jacobi weights 
$$w(x) = x^a (1 - x)^b {text{ (0}} < a,b < 1{text{)}}$$
. We obtain approximation equivalence theorems, using a weighted modulus of smoothness 
$$omega _{varphi ^lambda }^2 (f,t)_w $$
, which is an extension of~[5].
Keywords:weighted approximation  Bernstein operators  weighted modulus of smoothness
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