Open AccessStancu type generalization of Szász-Durrmeyer operators involving Brenke-type polynomials
Author(s) -
Rabi̇a Aktaş,
Dilek Söylemez,
Fatma Taşdelen
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1903855a
Subject(s) - mathematics , hermite polynomials , generalization , type (biology) , modulus of continuity , baskakov operator , orthogonal polynomials , classical orthogonal polynomials , order (exchange) , pure mathematics , rate of convergence , wilson polynomials , operator theory , convergence (economics) , discrete orthogonal polynomials , discrete mathematics , mathematical analysis , fourier integral operator , microlocal analysis , key (lock) , ecology , finance , economic growth , economics , biology
In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin?s theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance v. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance v, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.