On Koenigs' ratios for iterates of real functions
- 1 August 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 10 (1-2) , 207-213
- https://doi.org/10.1017/s1446788700007084
Abstract
In a recent note, M. Kuczama [5] has obtained a general result concerning real solutions φ(x) on the interval 0 ≦ x < a ≦∞ of the Schröder functional equation providing the known real function satisfies the following (quite weak) conditions: f(x) is continuous and strictly increasing in ([0 a);(0) = 0 and 0 <f(x) x→0+ {f(x)/x} = s; and f(x)/x is monotonic in (0, a).Keywords
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