A functional equation arising from an asymptotic formula for iterates

Detlef Gronau; Maciej Sablik

Published: 1994-09-30

Vol. 8 (1994)

A functional equation arising from an asymptotic formula for iterates

Detlef Gronau , Maciej Sablik

Abstract

We consider the real solutions of the functional equation
(⚹) ϕ^m(x) = 1/m ϕ(mx), ϕ(0) = 0,
where m∈ℕ and ϕ^m denotes the m-th iterate of the unknown function ϕ. We will handle this functional equation for a fixed m, but also for all naturals m, and give a representation of all C²-solutions (even weaker, see Theorem 2.1) of (⚹), but also treat the case of other solutions of this equation. In the introduction we will show the origin of this equation.

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Gronau, D., & Sablik, M. (1994). A functional equation arising from an asymptotic formula for iterates. Annales Mathematicae Silesianae, 8, 173–187. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14233

Detlef Gronau

Affiliation:

Institut für Mathematik, Universität Graz, Austria Austria

Maciej Sablik

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

Vol. 8 (1994)
Published: 1994-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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