Convergence of Certain Baskakov Operators of Integral Type

In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,∞) with the properties: φ(0)=0,φ′>0 on [0,∞) and limx→∞φ(x)=∞. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are stu...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-09, Vol.13 (9), p.1747
Main Authors: Birou, Marius Mihai, Muraru, Carmen Violeta, Radu, Voichiţa Adriana
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Baskakov operators
bounded variation
Convergence
Integrals
Mathematical analysis
Operators (mathematics)
Prairies
rate of convergence
Voronovskaja type theorems
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Summary:In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,∞) with the properties: φ(0)=0,φ′>0 on [0,∞) and limx→∞φ(x)=∞. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval (−∞,0] (the symmetric of the interval [0,∞) from the origin).
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13091747