𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Limits of (Linear Combinations of) Iterates of Linear Operators

✍ Scribed by Hans-Jörg Wenz

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
400 KB
Volume
89
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

We give necessary and sufficient conditions such that iterates or certain linear combinations of iterates of linear operators of finite dimensional range, respectively, converge. In case of convergence, we give an expression for the limit as well as estimates for the rate of convergence. Our results are then applied to Schoenberg type and SablonnieÁ re operators as well as tensor product Schoenberg type operators, Bernstein and Bernstein Durrmeyer operators over triangles. 1997 Academic Press several authors (see Chen and Feng [5] for an overview). On the other hand side, in 1973 Micchelli [15] introduced certain linear combinations of iterates of univariate Bernstein operators. These linear combinations can also be regarded as iterated Boolean sums M B n ( f ; } ), article no. AT963039 219

📜 SIMILAR VOLUMES

Lagrange and Least-Squares Polynomials a
Lagrange and Least-Squares Polynomials as Limits of Linear Combinations of Iterates of Bernstein and Durrmeyer Polynomials
✍ J.C. Sevy 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 139 KB

The linear combination of iterates \(1-\left(1-P_{n}\right)^{M}\) of Bernstein and Durrmeyer operators of a fixed degree \(n\) is considered for increasing order of iteration \(M\). The resulting sequence of polynomials is shown to converge to the Lagrange interpolating polynomial for the Bernstein

Pointwise Estimate for Linear Combinatio
Pointwise Estimate for Linear Combinations of Bernstein–Kantorovich Operators
✍ Shunsheng Guo; Lixia Liu; Qiulan Qi 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 115 KB

For linear combinations of Bernstein-Kantorovich operators K n r f x , we give an equivalent theorem with ω 2r ϕ λ f t . The theorem unites the corresponding results of classical and Ditzian-Totik moduli of smoothness.

On the Monotonicity of Positive Linear O
On the Monotonicity of Positive Linear Operators
✍ M.Kazim Khan; B. Della Vecchia; A. Fassih 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 377 KB

We provide sufficient conditions for a sequence of positive linear approximation operators, L n ( f, x), converging to f (x) from above to imply the convexity of f. We show that, for the convolution operators of Feller type, K n ( f, x), generated by a sequence of iid random variables taking values

The Characterization of the Derivatives
The Characterization of the Derivatives for Linear Combinations of Post–Widder Operators inLp
✍ Song Li; Ren Tai Wang 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 131 KB

The aim of the paper is to characterize the global rate of approximation of derivatives f (l) through corresponding derivatives of linear combinations of Post Widder operators in an appropriate weighted L p -metric using a weighted Ditzian and Totik modulus of smoothness, and also to characterize de