The iterates of positive linear operators preserving constants
β Scribed by Ioan Gavrea; Mircea Ivan
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 212 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
In this note we introduce a simple and efficient technique for studying the asymptotic behavior of the iterates of a large class of positive linear operators preserving constant functions.
π SIMILAR VOLUMES
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
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In the present paper, we study a new sequence of linear positive operators. We obtain a Voronovskaja type asymptotic formula and an estimate on error in terms of higher-order modulus of continuity for the iterative combinations of the new sequence of linear positive operators. Here, we also note tha