(p,q)-Generalization of Szász–Mirakjan operators and their approximation properties

We introduce a new modification of ( p , q ) -analogue of Szász–Mirakjan operators. Firstly, we give a recurrence relation for the moments of ( p , q ) -analogue of Szász–Mirakjan operators and present some explicit formulae for the moments and central moments up to order 4. Next, we obtain quantita...

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Bibliographic Details
Published in:Journal of inequalities and applications 2020-04, Vol.2020 (1), p.1-16, Article 116
Main Authors: Kara, Mustafa, Mahmudov, Nazim I.
Format: Article
Language:English
Subjects:
( p , q ) $(p,q)$ -Integers
( p , q ) $(p,q)$ -Szász–Mirakjan operators
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
Operators
Polynomials
Recent Advances in General Inequalities on Pure & Applied Mathematics and Related Areas
Weighted approximation
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Summary:We introduce a new modification of ( p , q ) -analogue of Szász–Mirakjan operators. Firstly, we give a recurrence relation for the moments of ( p , q ) -analogue of Szász–Mirakjan operators and present some explicit formulae for the moments and central moments up to order 4. Next, we obtain quantitative estimates for the convergence in the polynomial weighted spaces. In addition, we give the Voronovskaya theorem for the new ( p , q ) -Szász–Mirakjan operators.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02390-0