Stability of the Cauchy-Jensen functional equation in C*-algebras: A fixed point approach

Abstract

we prove the Hyers-Ulam-Rassias stability of C*-algebra homomorphisms and of generalized derivations on C*-algebras for the following Cauchy-Jensen functional equation 2f((x + y)/2 + z) = f(x) + f(y) + 2f(z), which was introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from the stability theorem of Th. M. Rassias that appeared in (1978).