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 ρ - functional inequalities in complex Banach spaces.