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In this paper, the authors have obtained the general solution of an octovigintic functional equation and proved its various stability results in the setting of Banach spaces, fuzzy normed spaces and random normed spaces using direct and fixed point methods. [ABSTRACT FROM AUTHOR]

In this paper, we prove the general solution and generalized Hyers–Ulam stability of n-dimensional functional equations of the form ∑ i = 1 i ≠ j ≠ k n f ⁢ ( - x i - x j - x k + ∑ l = 1 l ≠ i ≠ j ≠ k n x l ) = ( n 3 - 9 ⁢ n 2 + 20 ⁢ n - 12 6) ⁢ ∑ i = 1 n f ⁢ (x i) , \sum_{\begin{subarray}{c}i=1\\ i\neq j\neq k\end{subarray}}^{n}f\biggl{(}-x_{i}-x_{j}-x_{k}+\sum_{% \begin{subarray}{c}l=1\\ l\neq i\neq j\neq k\end{subarray}}^{n}x_{l}\biggr{)}=\biggl{(}\frac{n^{3}-9n^{% 2}+20n-12}{6}\biggr{)}\sum_{i=1}^{n}f(x_{i}), where n is a fixed positive integer with ℕ - { 0 , 1 , 2 , 3 , 4 } \mathbb{N}-\{0,1,2,3,4\} , in a Banach space via direct and fixed point methods. [ABSTRACT FROM AUTHOR]