Displaying similar documents to “Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness”

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...

Certain family of Durrmeyer type operators

Vijay Gupta (2009)

Annales UMCS, Mathematica

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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.