Quadratic $\rho$-functional inequalities and equations

Abstract

In this paper, we solve the quadratic $\rho$-functional inequalities where $\rho$ is a fixed complex number with $|\rho| where $\rho$ is a fixed complex number with $|\rho|< \frac{1}{2}$. 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.