3-Variable Additive rho-Functional Inequalities and Equations

Abstract

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