Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 1–16
Abstract
In the present paper, we establish direct and converse theorems for weighted
Bernstein-Durrmeyer operators under weighted $L^p$−norm with Jacobi weight $w(x) = x^{\alpha}(1−x)^{\beta}$. All the results involved have no restriction $\alpha$, $\beta<1-\frac{1}{p}$, which indicates
that the weighted Bernstein-Durrmeyer operators have some better approximation
properties than the usual Bernstein-Durrmeyer operators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2018.v34.n1.1
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 1–16
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Weighted $L^p$−approximation weighted Bernstein-Durrmeyer operators direct and converse theorems.