Solution of the ‘Cube’ Functional Equation in Terms of ‘Trilinear Coefficients’
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 181-191
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We consider the following three functional equations 1 2 3 where f:R3→R.Considering their geometric meaning, equations (1) and (2) are known as ‘Cube’ and ‘Octahedron’ functional equations, respectively. Under the assumption of continuity, Haruki [2] has proved that (1) and (2) are equivalent. Etigson [3], has proved the equivalence of (1) and (2) under no regularity assumption. We will give here another proof. Also, under the assumption of continuity, Haruki has solved the ‘Cube’ functional equation. He gave the solution as a certain polynomial of fifth degree in x, y, z individually whose terms are the partial derivatives of a given polynomial.
Hemdan, H. T. Solution of the ‘Cube’ Functional Equation in Terms of ‘Trilinear Coefficients’. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 181-191. doi: 10.4153/CMB-1976-028-5
@article{10_4153_CMB_1976_028_5,
author = {Hemdan, H. T.},
title = {Solution of the {{\textquoteleft}Cube{\textquoteright}} {Functional} {Equation} in {Terms} of {{\textquoteleft}Trilinear} {Coefficients{\textquoteright}}},
journal = {Canadian mathematical bulletin},
pages = {181--191},
year = {1976},
volume = {19},
number = {2},
doi = {10.4153/CMB-1976-028-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-028-5/}
}
TY - JOUR AU - Hemdan, H. T. TI - Solution of the ‘Cube’ Functional Equation in Terms of ‘Trilinear Coefficients’ JO - Canadian mathematical bulletin PY - 1976 SP - 181 EP - 191 VL - 19 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-028-5/ DO - 10.4153/CMB-1976-028-5 ID - 10_4153_CMB_1976_028_5 ER -
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