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On the iterates of positive linear operators preserving the affine functions

✍ Scribed by Ioan Gavrea; Mircea Ivan


Book ID
108178754
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
108 KB
Volume
372
Category
Article
ISSN
0022-247X

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The iterates of positive linear operator
✍ Ioan Gavrea; Mircea Ivan πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 212 KB

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.

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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