Geodesic
Lagrange-type Operators Associated with $U_n^{\varrho}$
Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 159 .

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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.
Classification : 41A36 41A05
Keywords: Bernstein operators, genuine Bernstein-Durrmeyer operators, Păltănea operators, Lagrange interpolation, eigenstructure, iterated Boolean sum, representation of derivatives 
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     author = {Heiner Gonska and Ioan Ra\c{s}a and Elena-Dorina St\u{a}nil\u{a}},
     title = {Lagrange-type {Operators} {Associated} with $U_n^{\varrho}$},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {159 },
     publisher = {mathdoc},
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     number = {110},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_96_110_a11/}
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Heiner Gonska; Ioan Raşa; Elena-Dorina Stănilă. Lagrange-type Operators Associated with $U_n^{\varrho}$. Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 159 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_96_110_a11/