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Regularly varying solutions of a linear functional equation

Published online by Cambridge University Press:  09 April 2009

Marek Kuczma
Marek Kuczma
Affiliation:
Mathematics Department, Silesian University Katowice, Poland.
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Abstract

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We are concerned with the problem of the existence and uniqueness of regularly varying (in Karamata's sense) solutions ϕ of the linear functional equation in a right neighbourhood of x = 0. Under suitable conditions on the given functions f and h, the uniqueness of solutions depends essentially on whether the series Σh ∘ f1 converges or diverges; here fi denotes the i-th functional iterate of f. The existence of solutions may be proved under further assumptions.

The case of the more general linear functional equation may be reduced to that of equation (*).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 135 - 143
Copyright
Copyright © Australian Mathematical Society 1976

References

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