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Note on Schröder's functional equation

Published online by Cambridge University Press:  09 April 2009

Marek Kuczma
Marek Kuczma
Affiliation:
Uniwersytet Jagielloński Kraków, Poland.
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In the present paper we are concerned with Schröder's functional equation , where ϕ(x) is the unknown function and is a number between 0 and 1: . We shall prove a theorem which generalizes some earlier results on convex solutions of the Schröder equation [4], [5].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 2 , May 1964 , pp. 149 - 151
Copyright
Copyright © Australian Mathematical Society 1964

References

[1] Fort, M. K. Jr, The embedding of homeomorphisms in flows, Proc. Amer. Math. Soc. 6 (1955), 960–967.CrossRefGoogle Scholar
[2] Kuczma, M., Remarques sur quelques théorèmes de J. Anastassiadis, Bull. Sci. Math. (2) 84 (1960), 98–102.Google Scholar
[3] Kuczma, M., Sur une équation fonctionnelle, Mathematica, Cluj, 3 (26) (1961), 79–87.Google Scholar
[4] Kuczma, M., A characterization of the exponential and logarithmic functions by functional equations, Fund. Math. 52 (1963), 283–288.CrossRefGoogle Scholar
[5] Kuczma, M., On the Schröder equation, Rozprawy Mat. 34 (1963).Google Scholar
[6] Lundberg, A., On iterated functions with asymptotic conditions at a fixpoint, Arhiv för Matematik, 5, (1963), 193–206.CrossRefGoogle Scholar
[7] Szekeres, G., Regular iteration of real and complex functions, Acta Math. 100, (1958), 203–258.CrossRefGoogle Scholar