Quadratic rho-functional inequalities in beta-homogeneous normed spaces

Abstract

In [12], Park introduced the quadratic p-functional inequalities parallel to f (x + y) + f (x - y) - 2f (x) 2f (y)parallel to (0.1) <=parallel to rho(2 f (x + y/2) + 2f (x - y/2) - f(x) - f(y))parallel to where rho is a fixed complex number with vertical bar rho vertical bar < 1, and parallel to 2f (x + y/2) +2f (x - y/2) - f (x) - f (y)parallel to (0.2) <=(rho f (x + y) + f (x - y) - 2f (x) - 2f (y))parallel to, where rho is a fixed complex number with vertical bar rho vertical bar < 1/2. 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.