Filomat 2023 Volume 37, Issue 5, Pages: 1523-1534
https://doi.org/10.2298/FIL2305523U
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Approximation properties of Bernstein-Stancu operators preserving e−2x
Usta Fuat (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Türkiye), fuatusta@duzce.edu.tr
Mursaleen Mohammad (Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan + Department of Mathematics, Aligarh Muslim University, Aligarh, India), mursaleenm@gmail.com
Çakır İbrahim (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Türkiye), suc.ceza0002@gmail.com
Bernstein-Stancu operators are one of the most powerful tool that can be used
in approximation theory. In this manuscript, we propose a new construction
of Bernstein-Stancu operators which preserve the constant and e−2x, x > 0.
In this direction, the approximation properties of this newly defined
operators have been examined in the sense of different function spaces. In
addition to these, we present the Voronovskaya type theorem for this
operators. At the end, we provide two computational examples to demonstrate
that the new operator is an approximation procedure.
Keywords: Linear positive operators, Benrstein-Stancu Operator, Exponential Functions, Approximation
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