3-Variable Additive rho-Functional Inequalities and Equations

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.This work was supported by the R&E program in 2013. C. Park (corresponding author) was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A2004299)