Operators Obtained by Using Certain Generating Function for Approximation

Serhan Varma and Sezgin Sucu
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Serhan Varma: Department of Mathematics, Faculty of Science, Ankara University, TR-06100 Ankara, Turkey
Sezgin Sucu: Department of Mathematics, Faculty of Science, Ankara University, TR-06100 Ankara, Turkey

Mathematics, 2022, vol. 10, issue 13, 1-9

Abstract: This paper is concerned with the sequence of positive linear operators obtained by certain generating functions of polynomials and with investigation of its approximation properties in detail. Initially, the convergence theorem is expressed for the sequence constructed in this article using the universal Korovkin-type theorem and then considering the modulus of continuity and the Lipschitz class, an estimate of the degree of approximation is obtained for this sequence of positive linear operators. Moreover, the generalization involving integral of these operators is defined and then their approximation properties are examined.

Keywords: Szasz operator; Szasz-Kantorovich operator; Brenke polynomials; Boas-Buck type polynomials; generating functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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