On Approximate Solutions of Functional Equations in Vector Lattices
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/547673 |
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| _version_ | 1832556448002867200 |
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| author | Bogdan Batko |
| author_facet | Bogdan Batko |
| author_sort | Bogdan Batko |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-06d58fb35e4a44a9bbb5abc1a2495302 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-06d58fb35e4a44a9bbb5abc1a24953022025-02-03T05:45:15ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/547673547673On Approximate Solutions of Functional Equations in Vector LatticesBogdan Batko0Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, PolandWe 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.http://dx.doi.org/10.1155/2014/547673 |
| spellingShingle | Bogdan Batko On Approximate Solutions of Functional Equations in Vector Lattices Abstract and Applied Analysis |
| title | On Approximate Solutions of Functional Equations in Vector Lattices |
| title_full | On Approximate Solutions of Functional Equations in Vector Lattices |
| title_fullStr | On Approximate Solutions of Functional Equations in Vector Lattices |
| title_full_unstemmed | On Approximate Solutions of Functional Equations in Vector Lattices |
| title_short | On Approximate Solutions of Functional Equations in Vector Lattices |
| title_sort | on approximate solutions of functional equations in vector lattices |
| url | http://dx.doi.org/10.1155/2014/547673 |
| work_keys_str_mv | AT bogdanbatko onapproximatesolutionsoffunctionalequationsinvectorlattices |