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

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, I-20133, Milano, Italia

    Gian Luigi Forti & Luigi Paganoni

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  1. Gian Luigi Forti
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  2. Luigi Paganoni
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Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth.

Partially supported by M.U.R.S.T. Research funds (40%)

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Forti, G.L., Paganoni, L. On an alternative cauchy equation in two unknown functions. Some classes of solutions. Aeq. Math. 42, 271–295 (1991). https://doi.org/10.1007/BF01818495

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  • DOI: https://doi.org/10.1007/BF01818495

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