an:05777296
Zbl 1203.39015
Cho, Yeol Je; Park, Choonkil; Saadati, Reza
Functional inequalities in non-Archimedean Banach spaces
EN
Appl. Math. Lett. 23, No. 10, 1238-1242 (2010).
00266266
2010
j
39B82 46S10 39B52 39B62
non-Archimedean Banach space; generalized Hyers-Ulam stability; Jordan-von Neumann functional equation; functional inequality
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.
Mohammad Sal Moslehian (Mashhad)