On the Stability of Quadratic Functional Equations
Let X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx+y)+f(kx-y)=2k2f(x)+2f(y) for all x,y∈X if and only if the mapping f:X→Y satisfies f(x+y)+f(x-y)=2f(x)+2f(y) for all x,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banac...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/628178 |
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| _version_ | 1832567085318799360 |
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| author | Jung Rye Lee Jong Su An Choonkil Park |
| author_facet | Jung Rye Lee Jong Su An Choonkil Park |
| author_sort | Jung Rye Lee |
| collection | DOAJ |
| description | Let X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx+y)+f(kx-y)=2k2f(x)+2f(y) for all x,y∈X if and only if the mapping f:X→Y satisfies f(x+y)+f(x-y)=2f(x)+2f(y) for all x,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven. |
| format | Article |
| id | doaj-art-2c305513ce404e5ab3928f0821248895 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2c305513ce404e5ab3928f08212488952025-02-03T01:02:19ZengWileyAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/628178628178On the Stability of Quadratic Functional EquationsJung Rye Lee0Jong Su An1Choonkil Park2Department of Mathematics, Daejin University, Kyeonggi 487-711, South KoreaDepartment of Mathematics Education, Pusan National University, Pusan 609-735, South KoreaDepartment of Mathematics, Hanyang University, Seoul 133-791, South KoreaLet X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx+y)+f(kx-y)=2k2f(x)+2f(y) for all x,y∈X if and only if the mapping f:X→Y satisfies f(x+y)+f(x-y)=2f(x)+2f(y) for all x,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.http://dx.doi.org/10.1155/2008/628178 |
| spellingShingle | Jung Rye Lee Jong Su An Choonkil Park On the Stability of Quadratic Functional Equations Abstract and Applied Analysis |
| title | On the Stability of Quadratic Functional Equations |
| title_full | On the Stability of Quadratic Functional Equations |
| title_fullStr | On the Stability of Quadratic Functional Equations |
| title_full_unstemmed | On the Stability of Quadratic Functional Equations |
| title_short | On the Stability of Quadratic Functional Equations |
| title_sort | on the stability of quadratic functional equations |
| url | http://dx.doi.org/10.1155/2008/628178 |
| work_keys_str_mv | AT jungryelee onthestabilityofquadraticfunctionalequations AT jongsuan onthestabilityofquadraticfunctionalequations AT choonkilpark onthestabilityofquadraticfunctionalequations |