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Pointwise weighted approximation by Bernstein operators

Authors:	Shunsheng Guo Hongzhi Tong Gengsheng Zhang

Institution:	(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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