Approximation of the generalized Cauchy-Jensen functional equation in C*-algebras

In this paper, we prove Hyers-Ulam-Rassias stability of C*-algebra homomorphisms for the following generalized Cauchy-Jensen equation: alpha mu f(x+y/alpha+z) = f(mu x) +f(mu y) + alpha f(mu z), for all mu is an element of S := {lambda is an element of C vertical bar vertical bar lambda vertical bar = 1} and for any fixed positive integer alpha >= 2, which was introduced by Gao et al. [J. Moth. Inequal. 3:63-77, 2009], on C*-algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers-Ulam-Rassias stability of generalized theta-derivation for such functional equations on C*-algebras by the same method.