- Tytuł:
- On some shift invariant integral operators, univariate case
- Autorzy:
-
Anastassiou, George
Gonska, Heinz - Powiązania:
- https://bibliotekanauki.pl/articles/1311499.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
global smoothness preservation
convergence to the unit with rates
Jackson type inequalities
sharp inequalities
modulus of continuity
integral operators
shift invariant operators
convolution type operators
shape preserving operators
probabilistic distribution function - Opis:
- In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and preservation of continuous probabilistic functions. Finally, four examples of very general specialized operators are presented fulfilling all the above properties; in particular, the inequalities for global smoothness preservation are proven to be sharp.
- Źródło:
-
Annales Polonici Mathematici; 1995, 61, 3; 225-243
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł