On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions
Annales Mathematicae Silesianae (2015)
- Volume: 29, Issue: 1, page 19-23
- ISSN: 0860-2107
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Abstract
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topKarol Baron. "On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions." Annales Mathematicae Silesianae 29.1 (2015): 19-23. <http://eudml.org/doc/276922>.
@article{KarolBaron2015,
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.},
author = {Karol Baron},
journal = {Annales Mathematicae Silesianae},
keywords = {orthogonal additivity; inner product space; continuous dependence on the given function; topological group; Tychonoff topology; nowhere dense set},
language = {eng},
number = {1},
pages = {19-23},
title = {On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions},
url = {http://eudml.org/doc/276922},
volume = {29},
year = {2015},
}
TY - JOUR
AU - Karol Baron
TI - On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions
JO - Annales Mathematicae Silesianae
PY - 2015
VL - 29
IS - 1
SP - 19
EP - 23
AB - 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.
LA - eng
KW - orthogonal additivity; inner product space; continuous dependence on the given function; topological group; Tychonoff topology; nowhere dense set
UR - http://eudml.org/doc/276922
ER -
References
top- [1] Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187–189. Zbl0840.39011
- [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. Zbl0569.39006
- [4] Sikorska J., Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215–277. Zbl1316.39008
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