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On a Relation between the “Square” Functional Equation And The “Square” Mean-Value Property

Published online by Cambridge University Press:  20 November 2018

Hiroshi Haruki
Hiroshi Haruki*
Affiliation:
University of Waterloo, Waterloo, Ontario
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We consider the following functional equation

1

where ƒ = ƒ(x, y) is a real-valued function of two real variables x, y on the whole xy-plane and t is a real variable.

With regard to the geometric meaning of (1), the equation is called the “square” functional equation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 161 - 165
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Aczél, J., Haruki, H., McKiernan, M. A., and Sakovič, G. N., General and regular solutions of functional equations characterizing harmonic polynomials, Aequationes Math. 1 (1968), 37-53.Google Scholar
2. Haruki, H., On a certain definite integral mean value problem (in Japanese), Sûgaku, 20 (1968), 165-166.Google Scholar
3. Światak, H., On the regularity of the distributional and continuous solutions of the functional equations , Aequationes Math. 1 (1968), 6-19.Google Scholar