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## Annales Mathematicae Silesianae

2017 | 31 | 57--62
Tytuł artykułu

### On Orthogonally Additive Functions With Big Graphs

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EN
Abstrakty
EN
Let $E$ be a separable real inner product space of dimension at least 2 and $V$ be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping $E$ into $V$ and having big graphs is dense in the space of all orthogonally additive functions from $E$ into $V$ with the Tychonoff topology. (original abstract)
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EN
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Tom
Strony
57--62
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autor
• University of Silesia in Katowice, Poland
Bibliografia
• Baron K., Orthogonally additive bijections are additive, Aequationes Math. 89 (2015), 297-299.
• Baron K., On the continuous dependence of solutions to orthogonal additivity problem on given functions, Ann. Math. Sil. 29 (2015), 19-23.
• Baron K., On orthogonally additive injections and surjections, Comment. Math. 55 (2015), 157-162.
• Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187-189.
• 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.
• Rätz J., On orthogonally additive mappings, Aequationes Math. 28 (1985), 35-49.
• Sikorska J., Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215-277.
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