Fixed points and stability of an additive functional equation of n-Apollonius type in C*-algebras

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of C*-algebra homomorphisms and of generalized derivations on C*-algebras for the following functional equation of Apollonius type Sigma(n)(i=1)f(z - x(i)) = -(1/n)Sigma(1 <= i<j <= n)f(x(i) + x(j)) + nf(z - (1/n(2))Sigma(n)(i=1)x(i)).