Non-Archimedean random stability of \(\sigma\)-quadratic functional equation (Q2826283)

The authors consider the functional equation: NEWLINE\[NEWLINE f(ax+by)=a^2g(x)+b^2h(y)+\frac{ab}{2}\left[f(x+y)-f(x+\sigma(y))\right] NEWLINE\]NEWLINE which is a generalization of the quadratic functional equation. Here \(f,g,h\) are unknown functions between non-Archimedean random normed (Banach) spaces and \(\sigma\) is an additive involution.NEWLINENEWLINEThe main result concerns the stability of the above equation. Using a fixed point theorem, the authors prove that each approximate solution of the equation can be (in a specific sense) approximated by a unique quadratic mapping.