aequationes mathematicae

, Volume 42, Issue 1, pp 271–295

# On an alternative cauchy equation in two unknown functions. Some classes of solutions

• Gian Luigi Forti
• Luigi Paganoni
Research Papers

## Summary

In this paper we consider the alternative Cauchy functional equationg(xy) ≠ g(x)g(y) impliesf(xy) = f(x)f(y) wheref, g are functions from a topological group (X, ·) into a group (S,·). First we prove that, ifS is a Hausdorff topological group andX satisfies some weak additional hypotheses, then (f, g) is a continuous solution if and only if eitherf org is a homomorphism. Then we describe a more general class of solutions forX =R n .

### AMS (1980) subject classification

Primary 39B30, 39B50, 39B70

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