Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations
Let 3โค๐, and 3โค๐โค๐ be positive integers. Let ๐ด be an algebra and let ๐ be an ๐ด-bimodule. A โ-linear mapping ๐โถ๐ดโ๐ is called a generalized (๐,๐)-derivation if there exists a (๐โ1)-derivation ๐ฟโถ๐ดโ๐ such that ๐(๐1๐2โฏ๐๐)=๐ฟ(๐1)๐2โฏ๐๐+๐1๐ฟ(๐2)๐3โฏ๐๐+โฏ+๐1๐2โฏ๐๐โ2๐ฟ(๐๐โ1)๐๐โฏ๐๐+๐1๐2โฏ๐๐โ1๐(๐๐)๐๐+1โฏ๐๐+๐1๐2โฏ๐๐๐(๐๐+...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/437931 |
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| author | M. Eshaghi Gordji J. M. Rassias N. Ghobadipour |
| author_facet | M. Eshaghi Gordji J. M. Rassias N. Ghobadipour |
| author_sort | M. Eshaghi Gordji |
| collection | DOAJ |
| description | Let 3โค๐, and 3โค๐โค๐ be positive integers. Let ๐ด be an algebra and let ๐ be an ๐ด-bimodule. A โ-linear
mapping ๐โถ๐ดโ๐ is called a generalized (๐,๐)-derivation if
there exists a (๐โ1)-derivation ๐ฟโถ๐ดโ๐ such that
๐(๐1๐2โฏ๐๐)=๐ฟ(๐1)๐2โฏ๐๐+๐1๐ฟ(๐2)๐3โฏ๐๐+โฏ+๐1๐2โฏ๐๐โ2๐ฟ(๐๐โ1)๐๐โฏ๐๐+๐1๐2โฏ๐๐โ1๐(๐๐)๐๐+1โฏ๐๐+๐1๐2โฏ๐๐๐(๐๐+1)๐๐+2โฏ๐๐+๐1๐2โฏ๐๐+1๐(๐๐+2)๐๐+3โฏ๐๐+โฏ+๐1โฏ๐๐โ1๐(๐๐) for all ๐1,๐2,โฆ,๐๐โ๐ด. The main purpose of this paper is
to prove the generalized Hyers-Ulam stability of the generalized
(๐,๐)-derivations. |
| format | Article |
| id | doaj-art-3e56ef2d69f9418dbd6fdabd22b007d1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3e56ef2d69f9418dbd6fdabd22b007d12025-08-20T03:55:41ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/437931437931Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-DerivationsM. Eshaghi Gordji0J. M. Rassias1N. Ghobadipour2Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, IranSection of Mathematics and Informatics, Pedagogical Department, National and Capodistrian University of Athens, 4, Agamemnonos St., Aghia Paraskevi, 15342 Athens, GreeceDepartment of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, IranLet 3โค๐, and 3โค๐โค๐ be positive integers. Let ๐ด be an algebra and let ๐ be an ๐ด-bimodule. A โ-linear mapping ๐โถ๐ดโ๐ is called a generalized (๐,๐)-derivation if there exists a (๐โ1)-derivation ๐ฟโถ๐ดโ๐ such that ๐(๐1๐2โฏ๐๐)=๐ฟ(๐1)๐2โฏ๐๐+๐1๐ฟ(๐2)๐3โฏ๐๐+โฏ+๐1๐2โฏ๐๐โ2๐ฟ(๐๐โ1)๐๐โฏ๐๐+๐1๐2โฏ๐๐โ1๐(๐๐)๐๐+1โฏ๐๐+๐1๐2โฏ๐๐๐(๐๐+1)๐๐+2โฏ๐๐+๐1๐2โฏ๐๐+1๐(๐๐+2)๐๐+3โฏ๐๐+โฏ+๐1โฏ๐๐โ1๐(๐๐) for all ๐1,๐2,โฆ,๐๐โ๐ด. The main purpose of this paper is to prove the generalized Hyers-Ulam stability of the generalized (๐,๐)-derivations.http://dx.doi.org/10.1155/2009/437931 |
| spellingShingle | M. Eshaghi Gordji J. M. Rassias N. Ghobadipour Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations Abstract and Applied Analysis |
| title | Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations |
| title_full | Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations |
| title_fullStr | Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations |
| title_full_unstemmed | Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations |
| title_short | Generalized Hyers-Ulam Stability of Generalized (๐,๐พ)-Derivations |
| title_sort | generalized hyers ulam stability of generalized ๐ ๐พ derivations |
| url | http://dx.doi.org/10.1155/2009/437931 |
| work_keys_str_mv | AT meshaghigordji generalizedhyersulamstabilityofgeneralizednkderivations AT jmrassias generalizedhyersulamstabilityofgeneralizednkderivations AT nghobadipour generalizedhyersulamstabilityofgeneralizednkderivations |