Geodesic
On a Relation between the “Square” Functional Equation And The “Square” Mean-Value Property
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 161-165

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Haruki, Hiroshi. On a Relation between the “Square” Functional Equation And The “Square” Mean-Value Property. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 161-165. doi: 10.4153/CMB-1971-030-6
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[1] 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] 2. Haruki, H., On a certain definite integral mean value problem (in Japanese), Sûgaku, 20 (1968), 165-166. Google Scholar

[3] 3. Światak, H., On the regularity of the distributional and continuous solutions of the functional equations , Aequationes Math. 1 (1968), 6-19. Google Scholar

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