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.

Convergence of iterates of linear operators and the Kelisky-Rivlin type theorems

Jacek Jachymski (2009)

Studia Mathematica

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Let X be a Banach space and T ∈ L(X), the space of all bounded linear operators on X. We give a list of necessary and sufficient conditions for the uniform stability of T, that is, for the convergence of the sequence ( T ⁿ ) n ∈ ℕ of iterates of T in the uniform topology of L(X). In particular, T is uniformly stable iff for some p ∈ ℕ, the restriction of the pth iterate of T to the range of I-T is a Banach contraction. Our proof is elementary: It uses simple facts from linear algebra, and the Banach...