Abstract
We study the eigenstructure of a one-parameter class of operators \({U_{n}^{\varrho}}\) of Bernstein–Durrmeyer type that preserve linear functions and constitute a link between the so-called genuine Bernstein–Durrmeyer operators U n and the classical Bernstein operators B n . In particular, for \({\varrho\rightarrow\infty}\) (respectively, \({\varrho=1}\)) we recapture results well-known in the literature, concerning the eigenstructure of B n (respectively, U n ). The last section is devoted to applications involving the iterates of \({U_{n}^{\varrho}}\).
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Gonska, H., Raşa, I. & Stănilă, ED. The Eigenstructure of Operators Linking the Bernstein and the Genuine Bernstein–Durrmeyer operators. Mediterr. J. Math. 11, 561–576 (2014). https://doi.org/10.1007/s00009-013-0347-0
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DOI: https://doi.org/10.1007/s00009-013-0347-0