Open Access
2014 On Approximate Solutions of Functional Equations in Vector Lattices
Bogdan Batko
Abstr. Appl. Anal. 2014: 1-10 (2014). DOI: 10.1155/2014/547673


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)0F(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.


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Bogdan Batko. "On Approximate Solutions of Functional Equations in Vector Lattices." Abstr. Appl. Anal. 2014 1 - 10, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022601
MathSciNet: MR3198212
Digital Object Identifier: 10.1155/2014/547673

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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