3-Variable Additive rho-Functional Inequalities and Equations

Abstract

In this paper, we introduce and investigate additive ρ-functional inequalities associated with the following additive functional equations f(x+y+z)?f(x)?f(y)?f(z)=02f(x+y/2+z)?f(x)?f(y)?2f(z)=02f(x+y+z/2)?f(x)?f(y)?f(z)=0 Furthermore, we prove the Hyers?Ulam stability of the additive ρ-functional inequalities in complex Banach spaces and prove the Hyers?Ulam stability of additive ρ-functional equations associated with the additive ρ-functional inequalities in complex Banach spaces.