Additive-quadratic ρ-functional equations in non-Archimedean Banach spaces

Abstract

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