Additive-quadratic ρ-functional inequalities in non-archimedean banach spaces

Abstract

Let (formula presented) We solve the additive-quadratic ρ-functional inequalities ‖M1f(x; y)‖ ≤ ‖ρM2f(x; y)‖, (0.1) where ρ is a fixed non-Archimedean number with |ρ| < 1, and ‖M2f(x; y)‖ ≤ ‖ρM1f(x; y)‖, (0.2) where ρ is a fixed non-Archimedean number with |ρ| < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.