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On Approximate Solutions of Functional Equations in Vector Lattices
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-06
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra).
The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations.
The idea is based on the use of the Spectral Representation Theory for Riesz spaces.
The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y)+F(x)+F(y)≠0⇒F(x+y)=F(x)+F(y) in Riesz spaces, the Cauchy equation with squares F(x+y)2=(F(x)+F(y))2 in f-algebras, and the quadratic functional equation F(x+y)+F(x-y)=2F(x)+2F(y) in Riesz spaces.
American Psychological Association (APA)
Batko, Bogdan. 2014. On Approximate Solutions of Functional Equations in Vector Lattices. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014211
Modern Language Association (MLA)
Batko, Bogdan. On Approximate Solutions of Functional Equations in Vector Lattices. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1014211
American Medical Association (AMA)
Batko, Bogdan. On Approximate Solutions of Functional Equations in Vector Lattices. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014211
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014211