Journal article
Some dynamically trivial mappings with applications to the improvement of simple iteration
Computers & mathematics with applications (1987), v 24(10)
1992
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Abstract
We consider the iteration algorithm defined by
x
n+k = g[φ(x
n, x
n+1,…,x
n+k−1)], n = 0,1,2,…,
where φ is a
k-dimensional means. We show that under certain conditions on the function
g, the algorithm will converge globally to a fixed point of
g, and that under less stringent conditions, it will converge locally, even when the corresponding algorithm for simple iteration,
x
n+1 = g (x
n), n = 0,1,2,…,
does not. A corollary of our main theorem answers a related question concerning the dynamic triviality of a class of mappings of
R
k
into itself.
Metrics
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4 citations in Scopus
Details
- Title
- Some dynamically trivial mappings with applications to the improvement of simple iteration
- Creators
- Bernhard Beckermann - Leibniz University HannoverJet Wimp - Drexel University
- Publication Details
- Computers & mathematics with applications (1987), v 24(10)
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1992JQ59600007
- Scopus ID
- 2-s2.0-38249010538
- Other Identifier
- 991019312453604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied