On Pexider Differences in Topological Vector Spaces
Let 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖<𝑑} where 𝑑>0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 𝐷1(𝐷2...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/370104 |
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| author | Abbas Najati M. R. Abdollahpour Gwang Hui Kim |
| author_facet | Abbas Najati M. R. Abdollahpour Gwang Hui Kim |
| author_sort | Abbas Najati |
| collection | DOAJ |
| description | Let 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖<𝑑} where 𝑑>0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 𝐷1(𝐷2), and taking values in 𝑌. We consider also the Pexiderized Cauchy functional equation. |
| format | Article |
| id | doaj-art-cc89a4ba73e34f6ebc76ae29e67f3e02 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cc89a4ba73e34f6ebc76ae29e67f3e022025-02-03T01:06:56ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/370104370104On Pexider Differences in Topological Vector SpacesAbbas Najati0M. R. Abdollahpour1Gwang Hui Kim2Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranDepartment of Applied Mathematics, Kangnam University, Gyeonggi, Giheung-gu, Yongin 446-702, Republic of KoreaLet 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖<𝑑} where 𝑑>0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 𝐷1(𝐷2), and taking values in 𝑌. We consider also the Pexiderized Cauchy functional equation.http://dx.doi.org/10.1155/2011/370104 |
| spellingShingle | Abbas Najati M. R. Abdollahpour Gwang Hui Kim On Pexider Differences in Topological Vector Spaces Abstract and Applied Analysis |
| title | On Pexider Differences in Topological Vector Spaces |
| title_full | On Pexider Differences in Topological Vector Spaces |
| title_fullStr | On Pexider Differences in Topological Vector Spaces |
| title_full_unstemmed | On Pexider Differences in Topological Vector Spaces |
| title_short | On Pexider Differences in Topological Vector Spaces |
| title_sort | on pexider differences in topological vector spaces |
| url | http://dx.doi.org/10.1155/2011/370104 |
| work_keys_str_mv | AT abbasnajati onpexiderdifferencesintopologicalvectorspaces AT mrabdollahpour onpexiderdifferencesintopologicalvectorspaces AT gwanghuikim onpexiderdifferencesintopologicalvectorspaces |