We prove that every bounded n -derivation of a commutative factorizable Banach algebra maps into its radical. Also, the nilpotency of eigenvectors of any bounded n -derivation corresponding to its eigenvalues is derived. We introduce the notion of approximate n -derivations on a Banach algebra A and show that the separating space of an approximate n -derivation ( n > 2 ) is not necessarily an ideal, unless the Banach algebra A is factorizable. From this and some results on bounded n -derivations, we prove that every approximate n -derivation of a semisimple factorizable Banach algebra is automatically continuous and every approximate n -derivation of a commutative semisimple factorizable Banach algebra is identically zero. Some applications of our results are also provided.
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