On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

Karol Baron

Annales Mathematicae Silesianae (2015)

  • Volume: 29, Issue: 1, page 19-23
  • ISSN: 0860-2107

Abstract

top
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.

How to cite

top

Karol 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. [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. [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. [3] Rätz J., On orthogonally additive mappings, Aequationes Math. 28 (1985), 35–49. Zbl0569.39006
  4. [4] Sikorska J., Orthogonalities and functional equations, Aequationes Math. 89 (2015), 215–277. Zbl1316.39008

NotesEmbed ?

top

You must be logged in to post comments.