Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I)
We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X→X and g:𝒜→𝒜. The mappings Δf,g1,&#x...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/718020 |
| _version_ | 1818139220319928320 |
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| author | Huai-Xin Cao Ji-Rong Lv J. M. Rassias |
| author_facet | Huai-Xin Cao Ji-Rong Lv J. M. Rassias |
| author_sort | Huai-Xin Cao |
| collection | DOAJ |
| description | We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X→X and g:𝒜→𝒜. The mappings Δf,g1, Δf,g2, Δf,g3, and Δf,g4 are defined and it is proved that if ∥Δf,g1(x,y,z,w)∥ (resp., ∥Δf,g3(x,y,z,w,α,β)∥) is dominated by φ(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 left derivation and g is a (resp., linear) module-X left derivation. It is also shown that if ∥Δf,g2(x,y,z,w)∥ (resp., ∥Δf,g4(x,y,z,w,α,β)∥) is dominated by φ(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 derivation and g is a (resp., linear) module-X derivation. |
| first_indexed | 2024-12-11T10:24:38Z |
| format | Article |
| id | doaj.art-6484b682950c4ea5a57616d6918f676b |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-11T10:24:38Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6484b682950c4ea5a57616d6918f676b2022-12-22T01:11:14ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-01200910.1155/2009/718020Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I)Huai-Xin CaoJi-Rong LvJ. M. RassiasWe discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X→X and g:𝒜→𝒜. The mappings Δf,g1, Δf,g2, Δf,g3, and Δf,g4 are defined and it is proved that if ∥Δf,g1(x,y,z,w)∥ (resp., ∥Δf,g3(x,y,z,w,α,β)∥) is dominated by φ(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 left derivation and g is a (resp., linear) module-X left derivation. It is also shown that if ∥Δf,g2(x,y,z,w)∥ (resp., ∥Δf,g4(x,y,z,w,α,β)∥) is dominated by φ(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 derivation and g is a (resp., linear) module-X derivation.http://dx.doi.org/10.1155/2009/718020 |
| spellingShingle | Huai-Xin Cao Ji-Rong Lv J. M. Rassias Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I) Journal of Inequalities and Applications |
| title | Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I) |
| title_full | Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I) |
| title_fullStr | Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I) |
| title_full_unstemmed | Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I) |
| title_short | Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I) |
| title_sort | superstability for generalized module left derivations and generalized module derivations on a banach module i |
| url | http://dx.doi.org/10.1155/2009/718020 |
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