Displaying similar documents to “Bernstein type operators having 1 and x j as fixed points”

Approximation by q -Bernstein type operators

Zoltán Finta (2011)

Czechoslovak Mathematical Journal

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Using the q -Bernstein basis, we construct a new sequence { L n } of positive linear operators in C [ 0 , 1 ] . We study its approximation properties and the rate of convergence in terms of modulus of continuity.

Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions

Heiner Gonska, Radu Păltănea (2010)

Czechoslovak Mathematical Journal

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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.