ADDITIVE rho-FUNCTIONAL INEQUALITIES IN MATRIX NORMED SPACES

Abstract

In [22], Kim et al. introduced and investigated the following additive rho-functional inequalities parallel to f(x+y+z) - f(x) - f(y) - f(z)parallel to (0.1) <=parallel to rho(2f(x+y/2+z) - f(x) - f(y) - 2f(z)parallel to, parallel to 2f(x+y/2+z) - f(x)-f(y) - 2f(z)parallel to (0.2) <=parallel to rho(2f(x+y+z/2) - f(x) - f(y) - f(z))parallel to in complex Banach spaces. We prove the Hyers-Ulam stability of the additive rho-functional inequalities (0.1) and (0.2) in complex matrix normed spaces and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (0.1) and (0.2) in complex matrix normed spaces.