Bernstein-Durrmeyer polynomials on a simplex
نویسندگان
چکیده
منابع مشابه
The Genuine Bernstein{Durrmeyer Operator on a Simplex
In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...
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For the Jacobi-type Bernstein–Durrmeyer operator Mn,κ on the simplex T d of R , we proved that for f ∈ L(Wκ ;T ) with 1 <p <∞, K2,Φ ( f,n−1 ) κ,p ≤ c‖f −Mn,κf ‖κ,p ≤ c′K2,Φ ( f,n−1 ) κ,p + c′n−1‖f ‖κ,p, where Wκ denotes the usual Jacobi weight on T d , K2,Φ(f, t)κ,p and ‖ · ‖κ,p denote the second-order Ditzian–Totik K-functional and the L-norm with respect to the weight Wκ on T d , respectively...
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*Correspondence: [email protected] College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, People’s Republic of China Abstract We give the direct and inverse approximation theorems for a new type of Bernstein-Durrmeyer operators with the mod...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1992
ISSN: 0021-9045
DOI: 10.1016/0021-9045(92)90104-v