A limit formula for regular iteration groups (Q1924296)
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scientific article; zbMATH DE number 935132
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A limit formula for regular iteration groups |
scientific article; zbMATH DE number 935132 |
Statements
A limit formula for regular iteration groups (English)
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21 April 1997
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The author offers a thorough survey and generalizations of results by \textit{G. Szekeres} [Acta Math. 100, 203-258 (1958; Zbl 0145.07903)], \textit{A. Lundberg} [Ark. Mat. 5, 193-206 (1964; Zbl 0196.45501)], \textit{G. Blanton} and \textit{J. A. Baker} [Arch. Math., Brno 18, 121-128 (1982; Zbl 0518.26002)], \textit{M. C. Zdun} [Aequationes Math. 28, 73-79 (1985; Zbl 0559.39003)] and \textit{L. Smolarek} [Zesz. Nauk. Wydz. Mat. Fiz. Chem., Mat., Gdańsk 7, 99-107 (1988; Zbl 0767.39002)] about automorphisms (bicontinuous bijections of a set onto itself) \(h\) of the set of positive numbers, without fixed points and for which \(h(x)/x\) has a finite right limit at 0 which is greater than 1 (the case where the limit is in \(]0,1[\) is similar). Several examples of applications and of the cases that can occur are also offered.
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regular iteration groups
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limits
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differentiable functions
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