Solution of a functional equation, connected with entropy, directed divergence, inaccuracy and their generalization of type β etc. is obtained without the assumption of any regularity condition on the functions involved.
Some elementary results on derivations of continuous fields of C*-algebras are used to prove that every derivation of an AW*-algebra of type III (or of type I) is inner, and also that if a given quotient of an AW*-algebra is known to have only inner derivations, its tensor product with a separable commutative C*-algebra with unit also has this property.