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Annales Mathematicae Silesianae

Editor-in-Chief: Sablik, Maciej

1 Issue per year


Mathematical Citation Quotient (MCQ) 2016: 0.10

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2391-4238
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On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

Karol Baron
Published Online: 2015-09-30 | DOI: https://doi.org/10.1515/amsil-2015-0002

Abstract

We show that the solution to the orthogonal additivity problem in real inner product spaces depends continuously on the given function and provide an application of this fact.

(2010) Mathematics Subject Classification:: 39B55; 39B52; 39B82

Key Words and phrases:: orthogonal additivity; inner product space; continuous dependence on the given function; topological group; Tychonoff topology; nowhere dense set

References

  • [1] Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187–189.Google Scholar

  • [2] Kuczma M., An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality, Second edition (edited by A. Gilányi), Birkhäuser Verlag, Basel, 2009.Google Scholar

  • [3] Rätz J., On orthogonally additive mappings, Aequationes Math. 28 (1985), 35–49.Google Scholar

  • [4] Sikorska J., Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215–277.Google Scholar

About the article

Received: 2014-09-10

Published Online: 2015-09-30

Published in Print: 2015-09-01


Citation Information: Annales Mathematicae Silesianae, Volume 29, Issue 1, Pages 19–23, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2015-0002.

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© Karol Baron. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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