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On additive solutions of a linear equation

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Abstract

We investigate the functional equation

$$ \sum\limits_{i = 1}^n {\alpha _i A(\beta _i x)} = 0 $$

which holds for all x ∈ ℝ with an unknown additive function A: ℝ → ℝ and fixed real parameters α i , β i , where i = 1; …; n. Here we give sufficient and necessary conditions for the existence of non-trivial additive solutions of the equation above in some cases depending on the algebraic properties of the parameters.

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References

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P. O. Box 12, Debrecen, Hungary

    A. Varga

Authors
  1. A. Varga
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Correspondence to A. Varga.

Additional information

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK-68040.

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Varga, A. On additive solutions of a linear equation. Acta Math Hung 128, 15–25 (2010). https://doi.org/10.1007/s10474-009-9148-0

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  • DOI: https://doi.org/10.1007/s10474-009-9148-0

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