Stability of quadratic functional equation in RN-spaces (Q2898675)

The authors consider the functional equation NEWLINE\[NEWLINE \sum_{1\leq i<j\leq m}f(x_i\pm x_j)=2(m-1)\sum_{i=1}^{m}f(x_i) NEWLINE\]NEWLINE (\(f: X\to Y\), \(X,Y\) vector spaces, \(m\geq 2\)) which appears to be equivalent to the quadratic functional equation: NEWLINE\[NEWLINE f(x+y)+f(x-y)=2f(x)+2f(y). NEWLINE\]NEWLINE The generalized Hyers-Ulam stability of the considered equation is proved for random normed (RN) spaces.