Additive rho-Functional Inequalities in beta-Homogeneous Normed Spaces

Abstract

In this paper, we solve the following additive rho-functional inequalities

parallel to f (x + y) - f (x) - f (y)parallel to <=parallel to rho(2f (x + y/2) - f (x) + -f (y)parallel to (1)

where rho is a fixed complex number with vertical bar rho vertical bar < 1, and

parallel to 2f (x + y/2) - f (x) - f (y)parallel to <=parallel to rho(f (x + y) - f (x) - f (y))parallel to (2)

where rho is a fixed complex number with vertical bar rho vertical bar < 1/2, and prove the Hyers-Ulam stability of the additive rho-functional inequalities (1) and (2) in beta-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (1) and (2) in beta-homogeneous complex Banach spaces.