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A Characterization of Exponential Functions with Non-Linear Exponents

Published online by Cambridge University Press:  20 November 2018

Halina Światak
Halina Światak*
Affiliation:
Université de Montréal, Montréal, Québec
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Extract

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It is well known (see e.g. [1]) that the Cauchy functional equation

characterizes the function f:x→exx.

It was mentioned in [2D that the functions f:x→A exp(αx2m), g:x→exx/A can be characterized by the equation

(1)

but the proof was done only for m=l which was considerably simple.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 277 - 281
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Aczél, J., Lectures on functional equations and their applications, Academic Press, New York and London, 1966.Google Scholar
2. Światak, H., On a class of functional equations with several unknown functions, Aequationes Math, (to appear).Google Scholar