Nearly Derivations on Banach Algebras
Let 𝑛 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆≠(𝑛2−𝑛+4)/2. We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖∑1≤𝑖<𝑗≤𝑛1≤𝑘𝑙≠𝑖,𝑗≤𝑛𝑓((𝑥𝑖+𝑥𝑗∑)/2+𝑛−2𝑙=1𝑥𝑘𝑙∑)+𝑓(𝑛𝑖=2𝑥𝑖)+𝑓(𝑥1∑)‖≤‖𝜆𝑓(𝑛𝑖=1𝑥...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/864340 |
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| author | M. Eshaghi Gordji H. Khodaei G. H. Kim |
| author_facet | M. Eshaghi Gordji H. Khodaei G. H. Kim |
| author_sort | M. Eshaghi Gordji |
| collection | DOAJ |
| description | Let 𝑛 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆≠(𝑛2−𝑛+4)/2. We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖∑1≤𝑖<𝑗≤𝑛1≤𝑘𝑙≠𝑖,𝑗≤𝑛𝑓((𝑥𝑖+𝑥𝑗∑)/2+𝑛−2𝑙=1𝑥𝑘𝑙∑)+𝑓(𝑛𝑖=2𝑥𝑖)+𝑓(𝑥1∑)‖≤‖𝜆𝑓(𝑛𝑖=1𝑥𝑖)‖. |
| format | Article |
| id | doaj-art-8a2cd391abc14615a9aec9ff58476094 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8a2cd391abc14615a9aec9ff584760942025-02-03T01:27:13ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/864340864340Nearly Derivations on Banach AlgebrasM. Eshaghi Gordji0H. Khodaei1G. H. Kim2Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranDepartment of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of KoreaLet 𝑛 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆≠(𝑛2−𝑛+4)/2. We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖∑1≤𝑖<𝑗≤𝑛1≤𝑘𝑙≠𝑖,𝑗≤𝑛𝑓((𝑥𝑖+𝑥𝑗∑)/2+𝑛−2𝑙=1𝑥𝑘𝑙∑)+𝑓(𝑛𝑖=2𝑥𝑖)+𝑓(𝑥1∑)‖≤‖𝜆𝑓(𝑛𝑖=1𝑥𝑖)‖.http://dx.doi.org/10.1155/2012/864340 |
| spellingShingle | M. Eshaghi Gordji H. Khodaei G. H. Kim Nearly Derivations on Banach Algebras Discrete Dynamics in Nature and Society |
| title | Nearly Derivations on Banach Algebras |
| title_full | Nearly Derivations on Banach Algebras |
| title_fullStr | Nearly Derivations on Banach Algebras |
| title_full_unstemmed | Nearly Derivations on Banach Algebras |
| title_short | Nearly Derivations on Banach Algebras |
| title_sort | nearly derivations on banach algebras |
| url | http://dx.doi.org/10.1155/2012/864340 |
| work_keys_str_mv | AT meshaghigordji nearlyderivationsonbanachalgebras AT hkhodaei nearlyderivationsonbanachalgebras AT ghkim nearlyderivationsonbanachalgebras |