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.
@article{bwmeta1.element.doi-10_1515_amsil-2015-0002,
author = {Karol Baron},
title = {On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions},
journal = {Annales Mathematicae Silesianae},
volume = {29},
year = {2015},
pages = {19-23},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0002}
}
Karol Baron. On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions. Annales Mathematicae Silesianae, Tome 29 (2015) pp. 19-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0002/
[1] Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187–189. | Zbl 0840.39011
[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. | Zbl 0569.39006
[4] Sikorska J., Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215–277. | Zbl 1316.39008