Quadratic \rho -functional inequalities and equations

In this paper, we solve the quadratic \rho -functional inequalities where \rho is a fixed complex number with , and where \rho is a fixed complex number with . Furthermore, we prove the Hyers-Ulam stability of the quadratic \rho -functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic \rho -functional equations associated with the quadratic \rho -functional inequalities (0.1) and (0.2) in complex Banach spaces.