Geodesic
A Functional Equation Arising from Ivory's Theorem in Geometry
Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 507-516

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

In previous papers (see [1, 2, 3, 4]), we solved the followingfunctional equation: 1 wheref=f(z) is an entire function of a complex variable z and x, y are complex variables. 
Haruki, Hiroshi. A Functional Equation Arising from Ivory's Theorem in Geometry. Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 507-516. doi: 10.4153/CMB-1975-093-8
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[1] 1. Haruki, Hiroshi, On Ivory’s Theorem, Mathematica Japonicae, 1 (1949) 151. Google Scholar

[2] 2. Haruki, Hiroshi, On the functional equations |f(x+iy)| = |f(x)+f(iy)| and |f(x+iy)| = |f(x) - f(iy)| and on Ivory’s Theorem, Canadian Mathematical Bulletin, 9 (1966) 473–480. Google Scholar

[3] 3. Haruki, Hiroshi, On parallelogram functional equations, Mathematische Zeitschrift, 104 (1968) 358–363. Google Scholar

[4] 4. Haruki, Hiroshi, On inequalities generalizing a functional equation connected with Ivory’s Theorem, American Mathematical Monthly, 75 (1968) 624–627. Google Scholar

[5] 5. Haruki, Hiroshi, An application of Picard’s Theorem to an extension of sine functional equations, Bulletin of the Calcutta Mathematical Society, 62 (1970) 129–132. Google Scholar

[6] 6. Zwirner, Kurt, Orthogonalsysteme, in denen Ivorys Theorem gilt, Abhand aus dem Hamburgischen Mathematischen Seminar, 5 (1926–27) 313–336. Google Scholar

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