A GENERAL ADDITIVE FUNCTIONAL INEQUALITY AND DERIVATION IN BANACH ALGEBRAS

초록

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 additive functional in-equality parallel to f(alpha x-beta y)- alpha f(x) beta f(-y)parallel to <= parallel to r(f(alpha x+ beta y) - beta f(y)parallel to, where r is a fixed nonzero complex number with vertical bar r vertical bar < 1 and alpha,beta not equal 0.

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