## Solutions of a non-homogeneous Cauchy equation.(English)Zbl 0697.39009

The author considers the following non-homogeneous Cauchy functional equation $$\phi (x_ 1+x_ 2)-\phi (x_ 1)-\phi (x_ 2)=d(x_ 1,x_ 2),$$ where d: $$G\times G\to B$$ is a given function satisfying certain solvability conditions and an unknown function $$\phi$$ is from an abelian group G into a Banach space B. The solutions of the equation above is given explicitly, assuming that d has a bounded Cauchy difference of some order.
Reviewer: M.C.Zdun

### MSC:

 39B99 Functional equations and inequalities 39B52 Functional equations for functions with more general domains and/or ranges