The Jensen functional equation in non-Archimedean normed spaces (Q1022911)

Summary: We investigate the Hyers-Ulam-Rassias stability of the Jensen functional equation in non-Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences. In particular, we show that a mapping \(f\) between non-Archimedean spaces with \(f(0) = 0\) is additive if and only if \[ \left\|f\;\frac{x+y}{2}-\frac{f(x)+f(y)}{2}\right\|\to 0 \] as \(\max\{\|x\|,\|y\|\}\to\infty\).