TY - JOUR
T1 - On Weighted $L^p$-Approximation by Weighted Bernstein-Durrmeyer Operators
JO - Analysis in Theory and Applications
VL - 1
SP - 1
EP - 16
PY - 2018
DA - 2018/07
SN - 34
DO - http://doi.org/10.4208/ata.2018.v34.n1.1
UR - https://global-sci.org/intro/article_detail/ata/12541.html
KW - Weighted $L^p$−approximation, weighted Bernstein-Durrmeyer operators, direct and converse theorems.
AB - <p style="text-align: justify;">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 $\alpha$, $\beta&lt;1-\frac{1}{p}$, which indicates
that the weighted Bernstein-Durrmeyer operators have some better approximation
properties than the usual Bernstein-Durrmeyer operators.<br/></p>