quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces

in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right| && qquad le  |rho(f(x+y)+f(x-y)-2f(x)-2f(y))|   , nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|in this paper, we prove the hyers-ulam stability of the quadratic $rho$-functional inequalities (0.1) and (0.2)  in $beta$-homogeneous 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 $beta$-homogeneous complex banach spaces.