Geodesic
A multi-dimensional functional equation having cubic forms as solutions
Park, Won-Gil1 ; Bae, Jae-Hyeong2
1 Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea
2 Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5238-5244.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we obtain some results on the m-variable cubic functional equation
$f(2x_1 + y_1,..., 2x_m + y_m) + f(2x_1 - y_1,..., 2x_m - y_m)\\ = 2f(x_1 + y_1,..., x_m + y_m) + 2f(x_1 - y_1,..., x_m - y_m) + 12f(x_1,..., x_m).$
The cubic form $f(x_1,..., x_m) = \sum_{1\leq i\leq j\leq k\leq m} a_{ijk}x_ix_jx_k$ is a solution of the above functional equation.
DOI : 10.22436/jnsa.009.08.09
Classification : 39B52, 39B82
Keywords: Cubic form, solution, stability.

Park, Won-Gil 1 ; Bae, Jae-Hyeong 2

1 Department of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea
2 Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea 
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Park, Won-Gil; Bae, Jae-Hyeong. A multi-dimensional functional equation having cubic forms as solutions. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5238-5244. doi : 10.22436/jnsa.009.08.09. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.08.09/

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