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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
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