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 for x ∈ (0, a); limx→0+ {f(x)/x} = s; and f(x)/x is monotonic in (0, a).
Publisher
Cambridge University Press (CUP)
Reference8 articles.
1. On iterated functions with asymptotic conditions at a fixpoint
2. Note on Schröder's functional equation
3. A survey of the theory of functional equations;Kuczma;Publikacije Elektrohnickog Fakultela, Univerzitet u Beogradu, Serija: Matematika i Fizika,1964
4. Reelle analytische Lösungen der Gleichungφ(φ(x)) = ex und verwandter Funktionalgleichungen;Kneser;J. reine angew. Math.,1950
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