Additive $ \rho $-functional inequalities in non-Archimedean 2-normed spaces

In this paper, we solve the additive $ \rho $-functional inequalities:where $ \rho $ is a fixed non-Archimedean number with $ |\rho| < 1 $. More precisely, we investigate the solutions of these inequalities in non-Archimedean $ 2 $-normed spaces, and prove the Hyers-Ulam stability of these inequalities in non-Archimedean $ 2 $-normed spaces. Furthermore, we also prove the Hyers-Ulam stability of additive $ \rho $-functional equations associated with these inequalities in non-Archimedean $ 2 $-normed spaces.