On Weighted LP-Approximation by Weighted Bernstein-Durrmeyer Operators

摘要

In the present paper,we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted Lp-norm with Jacobi weight w(x) =xα (1-x)β.All the results involved have no restriction α,β ＜ 1-1/p,which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.