Functional inequalities in non-Archimedean Banach spaces (Q990799)

The authors show that if \(f\) is a function between non-Archimedean spaces satisfying the functional inequality \(\|f(x)+f(y)+f(z)\| \leq \|k f((x+y+z)/k)\|\), where \(|k| < |3|\), then \(f\) is additive. They also prove the generalized Hyers-Ulam stability of the functional inequality above in non-Archimedean normed spaces. Reviewer's Comment: The authors assume that the domain of \(f\) is non-Archimedean, but it seems that they do not need this assumption.