Hom-derivations in C*-ternary Algebras

Abstract

In this paper, we introduce and solve the following additive (rho(1), rho(2))-functional inequalities

parallel to f(x + y + z) - f(x) - f(y) - f(z)parallel to

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

where rho(1) and rho(2) are fixed nonzero complex numbers with vertical bar rho(1)vertical bar + vertical bar rho(2)vertical bar < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the above additive (rho(1), rho(2))functional inequality in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in C*-ternary algebras.