APPROXIMATION THEOREMS FOR LIMIT $(p,q)-$BERNSTEIN-DURRMEYER OPERATOR
نویسندگان
چکیده
منابع مشابه
Approximation by the Bernstein–Durrmeyer Operator on a Simplex
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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We give a generalisation of the multivariate beta integral. This is used to show that the (multivariate) Bernstein–Durrmeyer operator for a Jacobi weight has a limit as the weight becomes singular. The limit is an operator previously studied by Goodman and Sharma. From the elementary proof given, it follows that this operator inherits many properties of the Bernstein–Durrmeyer operator in a nat...
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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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ژورنال
عنوان ژورنال: Facta Universitatis, Series: Mathematics and Informatics
سال: 2017
ISSN: 2406-047X,0352-9665
DOI: 10.22190/fumi1702195f