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.
 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.