ADDITIVE ρ-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES

In this paper, we solve the additive rho-functional inequalities parallel to f(x+y) - f(x) - f(y)parallel to <= parallel to rho (2f(x +y/2) - f(x) - f(y))parallel to parallel to 2f(x + y)/2) - f(x) - f(y)parallel to <= parallel to rho (f(x + y) - f(x) - f(y))parallel to, where rho is a fixed non-Archimedean number with vertical bar rho vertical bar < 1. Furthermore, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.