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

• Autorzy: Karol Baron
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

orthogonal additivity; inner product space; continuous dependence on the given function; topological group; Tychonoff topology; nowhere dense set

Kategorie tematyczne

• 39B55: Orthogonal additivity and other conditional equations
• 39B82: Stability, separation, extension, and related topics
• 39B52: Equations for functions with more general domains and/or ranges

• Wydawca: De Gruyter Open
• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Numer: 1
• Strony: 19-23

Daty

wydano

2015-09-01

otrzymano

2014-09-10

online

2015-09-30

Twórcy

autor

Karol Baron

• Institute of Mathematics, University of Silesia, Bankowa 14 40-007 Katowice, Poland

Bibliografia

• [1] Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187–189.
• [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.

Identyfikatory

DOI

10.1515/amsil-2015-0002