C*-TERNARY HOMOMORPHISMS, C*-TERNARY DERIVATIONS, JB*-TRIPLE HOMOMORPHISMS AND JB*-TRIPLE DERIVATIONS

Abstract

Park and Rassias proved the superstability of C*-ternary homomorphisms, C*-ternary derivations, JB*-triple homomorphisms and JB*-triple derivations, associated with the following Apollonius type additive functional equation f(z - x) + f(z - y) = - 1/2 f(x + y) + 2f (z - x + y/4) by using direct method. Under the conditions of the theorems, we can show that the mappings f must be zero. In this paper, we correct the conditions. Furthermore, we prove the superstability of C*-ternary homomorphisms, C*-ternary derivations, JB*-triple homomorphisms and JB*-triple derivations by using fixed point method.