The Jensen functional equation in non-Archimedean normed spaces

摘要

We investigate the Hyers–Ulam–Rassias stability of the Jensenfunctional equation in non-Archimedean normed spaces and study its asymptoticbehavior in two directions: bounded and unbounded Jensen differences. Inparticular, we show that a mappingfbetween non-Archimedean spaces withf(0)=0is additive if and only if‖f(x+y2)?f(x)+f(y)2‖→0as max{‖x‖,‖y‖}→∞.