Aequationes mathematicae

, Volume 89, Issue 2, pp 297–299 | Cite as

Orthogonally additive bijections are additive

  • Karol Baron
Open Access


Any orthogonally additive injection of a real inner product space of dimension at least 2 onto an abelian group is additive.

Mathematics Subject Classification (2010)

39B55 46C99 


Orthogonally additive and additive function inner product space 


  1. 1.
    Baron K.: On some orthogonally additive functions on inner product spaces. Ann. Univ. Budapest. Sect. Comput. 40, 123–127 (2013)MATHMathSciNetGoogle Scholar
  2. 2.
    Baron K., Rätz J.: On orthogonally additive mappings on inner product spaces. Bull. Polish Acad. Sci. Math. 43, 187–189 (1995)MATHMathSciNetGoogle Scholar
  3. 3.
    Rätz J.: On orthogonally additive mappings. Aequationes Math. 28, 35–49 (1985)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2013

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Instytut MatematykiUniwersytet Śla̧skiKatowicePoland

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