Generalized Hyers-Ulam stability for general additive functional equations in quasi-\(\beta \)-normed spaces
The authors investigate the generalized Hyers-Ulam stability problem for the following functional equation \[ \displaystyle\sum_{1\leq i \leq j\leq n}g\left(\frac{x_i+x_j}{2}+\displaystyle\sum_{l=1,k_l\neq i,j}^{n-2}x_{k_l}\right) =\frac{(n-1)^2}{2}\displaystyle\sum_{i=1}^{n}g(x_i), \] where \(n \geq 3\), \(g:X\to Y\) is a mapping and \(X\), \(Y\) are normed spaces. They also investigate this problem, when \(X\) is a quasi-\(\beta\) normed space.
scientific article; zbMATH DE number 5563870
scientific article