Displaying similar documents to “Limit semigroups of Bernstein-Schnabl operators associated with positive projections”

Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness

Francesco Altomare (2009)

Bollettino dell'Unione Matematica Italiana

Similarity:

Of concern are Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. With respect to these sequences of positive linear operators we determine the classes of all continuous functions verifying a pointwise asymptotic formula or a uniform one. Our methods are essentially based on a general characterization of the domains of Feller semigroups in terms of asymptotic formulae and on the determination of both the saturation class of Bernstein-Schnabl...

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

Jacek Jachymski (2009)

Studia Mathematica

Similarity:

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...

Certain family of Durrmeyer type operators

Vijay Gupta (2009)

Annales UMCS, Mathematica

Similarity:

The present paper is a continuation of the earlier work of the author. Here we study the rate of convergence of certain Durrmeyer type operators for function having derivatives of bounded variation.

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

Heiner Gonska, Radu Păltănea (2010)

Czechoslovak Mathematical Journal

Similarity:

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.