On the continuous dependence of solutions to orthogonal additivity problem on given functions
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.
Keywords
orthogonal additivity; inner product space; continuous dependence on the given function; topological group; Tychonoff topology; nowhere dense set
References
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.
3. Rätz J., On orthogonally additive mappings, Aequationes Math. 28 (1985), 35–49.
4. Sikorska J., Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215–277.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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