Hyers-Ulam Stability of General Jensen-Type Mappings in Banach Algebras

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of homomorphisms in complex Banach algebras and complex Banach Lie algebras and also of derivations on complex Banach algebras and complex Banach Lie algebras for the general Jensen-type functional equation f(alpha x + beta y) + f(alpha x - beta y) = 2 alpha f(x) for any with alpha, beta is an element of R with alpha, beta not equal 0. Furthermore, we prove the hyperstability of homomorphisms in complex Banach algebras for the above functional equation with alpha = beta = 1.