EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 96[110], pp. 159–168 (2014)

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LAGRANGE-TYPE OPERATORS ASSOCIATED WITH $U_n^{\varrho}$

Heiner Gonska, Ioan Rasa, and Elena-Dorina Stanila

University of Duisburg-Essen, Faculty of Mathematics, Duisburg, Germany and Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania

Abstract: We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein–Durrmeyer mappings. The focus is on their relation to certain Lagrange-type interpolators associated to them, a well known feature in the theory of Bernstein operators. Considerations concerning iterated Boolean sums and the derivatives of the operator images are included. Our main tool is the eigenstructure of the members of the class.

Keywords: Bernstein operators, genuine Bernstein-Durrmeyer operators, Paltanea operators, Lagrange interpolation, eigenstructure, iterated Boolean sum, representation of derivatives

Classification (MSC2000): 41A36; 41A05

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Electronic fulltext finalized on: 30 Oct 2014. This page was last modified: 24 Nov 2014.

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