3-variable Jensen ρ -functional inequalities and equations

In this paper, we introduce and investigate Jensen ρ-functional inequalities associated with the following Jensen functional equations f(x+ y + z) + f(x+ y − z)− 2f(x)− 2f(y) = 0, f(x+ y + z)− f(x− y − z)− 2f(y)− 2f(z) = 0. We prove the Hyers-Ulam-Rassias stability of the Jensen ρ-functional inequalities in complex Banach spaces and prove the Hyers-Ulam-Rassias stability of the Jensen ρ-functional equations associated with the ρfunctional inequalities in complex Banach spaces. c ©2016 All rights reserved.