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Composition of integral-type operators and discrete operators involving Laguerre polynomials

In this note we provide a new way to capture operators involving Laguerre polynomials by composition of an integral operator and a discrete operator. The new operator so obtained is a discrete operator. We give three examples by considering composition of Szász-Durrmeyer operator, exponential-type o...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2024-07, Vol.28 (3), p.39, Article 39
Main Authors: Abel, Ulrich, Gupta, Vijay
Format: Article
Language:English
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Summary:In this note we provide a new way to capture operators involving Laguerre polynomials by composition of an integral operator and a discrete operator. The new operator so obtained is a discrete operator. We give three examples by considering composition of Szász-Durrmeyer operator, exponential-type operator related to 2 x 3 / 2 and the Phillips operator, respectively, with Szász-Mirakyan operators. In all cases we obtain positive linear, discretely defined operators which are based on Laguerre polynomials and approximate functions on the positive real half-axis.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-024-01058-z