On problems of B. Choczewski and M. Kuczma concerning an integral equation
The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.
We generalize the well known separation theorems for subadditive and superadditive functionals to some classes of not necessarily Abelian semigroups. We also consider the problem of supporting subadditive functionals by additive ones in the not necessarily commutative case. Our results are motivated by similar extensions of the Hyers stability theorem for the Cauchy functional equation. In this context the so-called weakly commutative and amenable semigroups appear naturally. The relations between...