TY - JOUR
T1 - Direct, Inverse Theorems of Approximation by Linear Combinations of Weighted Baskakov–Durrmeyer Operators in Orlicz Spaces
AU - Han , Lingxiong
AU - Bai , Yumei
JO - Analysis in Theory and Applications
VL - 3
SP - 221
EP - 239
PY - 2024
DA - 2024/10
SN - 40
DO - http://doi.org/10.4208/ata.OA-2022-0013
UR - https://global-sci.org/intro/article_detail/ata/23466.html
KW - Direct theorem, inverse theorem, equivalent theorem, approximation, $K$-functional, Orlicz space, Jacobi weight, Baskakov–Durrmeyer operator.
AB - <p style="text-align: justify;">In the paper, the authors introduce the Orlicz space corresponding to the
Young function and, by virtue of the equivalent theorem between the modified $K$-functional and modulus of smoothness, establish the direct, inverse, and equivalent
theorems for the linear combinations of Jacobi weighted Baskakov–Durrmeyer operators in the Orlicz spaces.</p>