automatic continuity of surjective almost derivations on frechet q-algebras

In 1971 r. l. carpenter proved that every derivation t on a semisimple commutative frechet algebra ʌ with identity is continuous. by relaxing the commutativity assumption on ʌ and adding the surjectivity assumption on t, we derive a corresponding continuity result, for a new concept of almost derivations on frechet algebras in this article. also, it is further proved that every surjective almost derivation t on non commutative semisimple frechet q-algebras ʌ with an additional condition on ʌ, is continuous. moreover, an example is provided to illustrate our main result.