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On a quadratic difference assuming three values

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Abstract

The aim of this work is to investigate the alternative quadratic functional equation

$$\begin{aligned} f(x+y)+f(x-y)-2f(x)-2f(y)\in \{0,1,2\}, \end{aligned}$$

where \(f{: }G \rightarrow \mathbb {R}\), G is an Abelian group, and provide a procedure for the construction of the solutions.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini, 50, 20133, Milano, Italy

    Gian Luigi Forti

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  1. Gian Luigi Forti
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Correspondence to Gian Luigi Forti.

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Dedicated to Professor Karol Baron on the occasion of his 70th birthday, with esteem and friendship.

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Forti, G.L. On a quadratic difference assuming three values. Aequat. Math. 93, 161–203 (2019). https://doi.org/10.1007/s00010-018-0587-y

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  • DOI: https://doi.org/10.1007/s00010-018-0587-y

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