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A Characterization of Exponential Functions with Non-Linear Exponents
Published online by Cambridge University Press: 20 November 2018
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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
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- 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
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