Geodesic
Stability of an $l$-Variable Cubic Functional Equation
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 6, p. 851

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Using the direct and fixed point methods, we obtain the solution and prove the Hyers-Ulam stability of the $l$-variable cubic functional equation \begin{align*} (um_{i=1}^{l}x_i\right)+um_{j=1}^{l}feft(-lx_j+um_{i=1,ieq j}^{l}x_i\right) =-2(l+1)um_{i=1,ieq jeq k}^{l}f(x_i+x_j+x_k) +(3l^2-2l-5)um_{i=1,ieq j}^{l}f(x_i+x_j) -3(l^3-l^2-l+1)um_{i=1}^{l}f(x_i), \end{align*} $l\in {\mathbb{N}}$, $l\geq 3$, in random normed spaces.
Classification : 39B52, 47H10, 39B72, 39B82
Keywords: Cubic functional equation, fixed point, Hyers-Ulam stability, random normed space 
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     title = {Stability of an $l${-Variable} {Cubic} {Functional} {Equation}},
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Vediyappan Govindan; Sandra Pinelas; Jung Rye Lee; Choonkil Park. Stability of an $l$-Variable Cubic Functional Equation. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 6, p. 851 . http://geodesic.mathdoc.fr/item/KJM_2023_47_6_a2/