Acta Mathematica Vietnamica
Search within journal
Volumes and issues
STABILITY OF FUNCTIONAL EQUATIONS OF SEVERAL VARIABLES WHICH ARE ADDITIVE OR QUADRATIC IN EACH VARIABLES IN FRÉCHET SPACES
MADJID ESHAGHI GORDJI, ALI EBADIAN, RASOUL AGHALARYpp. 189-200
Abstract
In this paper, we establish the Hyers–Ulam–Rassias stability of the system of functional equations $$\begin{cases} f(x_1, x_2, \dots, x_{i_r−1}, a + b, x_{i_r+1}, \dots, x_n) = f(x_1, x_2, \dots, x_{i_r−1}, a, x_{i_r+1}, \dots, x_n) \\ +f(x_1, x_2, \dots, x_{i_r−1}, b, x_{i_r+1}, \dots, x_n), \\ f(x_1, x_2, \dots, x_{j_s−1}, a + b, x_{j_s+1}, \dots, x_n) + f(x_1, x_2, \dots, x_{j_s−1}, a − b, x_{j_s+1}, \dots, x_n)\\ = 2f(x_1, x_2, \dots, x_{j_s−1}, a, x_{j_s+1}, \dots, xn) + 2f(x_1, x_2, \dots, x_{j_s−1}, b, x_{j_s+1}, \dots, x_n)\end{cases}$$ in Fréchet spaces, where $1 \leq i_1 < i_2 < \dots < i_k < n,$ $1 < j_1 < j_2 < \dots < j_{n−k},$ ${1, 2, \dots, n} = \{i_1, i_2, \dots, i_k\} \cup \{j_1, j_2, \dots, j_{n−k}\}$.