Geodesic
Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 783-799.

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We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
Classification : 41A10, 41A17, 41A25, 41A28, 41A36, 41A60
Keywords: positive linear operator; Bernstein-type operator; genuine Bernstein-Durrmeyer operator; simultaneous approximation; degree of approximation; moduli of continuity 
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     title = {Simultaneous approximation by a class of {Bernstein-Durrmeyer} operators preserving linear functions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {783--799},
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     volume = {60},
     number = {3},
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     zbl = {1224.41016},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a12/}
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Gonska, Heiner; Păltănea, Radu. Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 783-799. http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a12/