Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation
Let 𝐴 be an algebra, and let 𝜃, 𝜙 be ring automorphisms of 𝐴. An additive mapping 𝐻∶𝐴→𝐴 is called a (𝜃,𝜙)-derivation if 𝐻(𝑥𝑦)=𝐻(𝑥)𝜃(𝑦)+𝜙(𝑥)𝐻(𝑦) for all 𝑥,𝑦∈𝐴. Moreover, an additive mapping 𝐹∶𝐴→𝐴 is said to be a generalized (𝜃,𝜙)-derivation if there exists a (𝜃,𝜙)-derivation 𝐻∶𝐴→𝐴 such that 𝐹(𝑥𝑦)=𝐹(𝑥...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/726020 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551006358994944 |
|---|---|
| author | M. Eshaghi Gordji M. B. Ghaemi G. H. Kim Badrkhan Alizadeh |
| author_facet | M. Eshaghi Gordji M. B. Ghaemi G. H. Kim Badrkhan Alizadeh |
| author_sort | M. Eshaghi Gordji |
| collection | DOAJ |
| description | Let 𝐴 be an algebra, and let 𝜃, 𝜙 be ring automorphisms of 𝐴. An additive
mapping 𝐻∶𝐴→𝐴 is called a (𝜃,𝜙)-derivation if 𝐻(𝑥𝑦)=𝐻(𝑥)𝜃(𝑦)+𝜙(𝑥)𝐻(𝑦) for all 𝑥,𝑦∈𝐴. Moreover, an additive mapping 𝐹∶𝐴→𝐴 is said to be a generalized (𝜃,𝜙)-derivation if there exists a (𝜃,𝜙)-derivation 𝐻∶𝐴→𝐴 such that 𝐹(𝑥𝑦)=𝐹(𝑥)𝜃(𝑦)+𝜙(𝑥)𝐻(𝑦) for all 𝑥,𝑦∈𝐴. In this paper, we investigate the superstability of generalized (𝜃,𝜙)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation. |
| format | Article |
| id | doaj-art-c896fec08ec34b68a7c503c325cb2fc4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c896fec08ec34b68a7c503c325cb2fc42025-02-03T06:05:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/726020726020Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional EquationM. Eshaghi Gordji0M. B. Ghaemi1G. H. Kim2Badrkhan Alizadeh3Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranDepartment of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranDepartment of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of KoreaTechnical and Vocational Faculty of Tabriz, Technical and Vocational University of Iran, P.O. Box 51745-135, Tabriz, IranLet 𝐴 be an algebra, and let 𝜃, 𝜙 be ring automorphisms of 𝐴. An additive mapping 𝐻∶𝐴→𝐴 is called a (𝜃,𝜙)-derivation if 𝐻(𝑥𝑦)=𝐻(𝑥)𝜃(𝑦)+𝜙(𝑥)𝐻(𝑦) for all 𝑥,𝑦∈𝐴. Moreover, an additive mapping 𝐹∶𝐴→𝐴 is said to be a generalized (𝜃,𝜙)-derivation if there exists a (𝜃,𝜙)-derivation 𝐻∶𝐴→𝐴 such that 𝐹(𝑥𝑦)=𝐹(𝑥)𝜃(𝑦)+𝜙(𝑥)𝐻(𝑦) for all 𝑥,𝑦∈𝐴. In this paper, we investigate the superstability of generalized (𝜃,𝜙)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.http://dx.doi.org/10.1155/2011/726020 |
| spellingShingle | M. Eshaghi Gordji M. B. Ghaemi G. H. Kim Badrkhan Alizadeh Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation Journal of Applied Mathematics |
| title | Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation |
| title_full | Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation |
| title_fullStr | Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation |
| title_full_unstemmed | Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation |
| title_short | Stability and Superstability of Generalized (𝜃, 𝜙)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation |
| title_sort | stability and superstability of generalized 𝜃 𝜙 derivations in non archimedean algebras fixed point theorem via the additive cauchy functional equation |
| url | http://dx.doi.org/10.1155/2011/726020 |
| work_keys_str_mv | AT meshaghigordji stabilityandsuperstabilityofgeneralizedθφderivationsinnonarchimedeanalgebrasfixedpointtheoremviatheadditivecauchyfunctionalequation AT mbghaemi stabilityandsuperstabilityofgeneralizedθφderivationsinnonarchimedeanalgebrasfixedpointtheoremviatheadditivecauchyfunctionalequation AT ghkim stabilityandsuperstabilityofgeneralizedθφderivationsinnonarchimedeanalgebrasfixedpointtheoremviatheadditivecauchyfunctionalequation AT badrkhanalizadeh stabilityandsuperstabilityofgeneralizedθφderivationsinnonarchimedeanalgebrasfixedpointtheoremviatheadditivecauchyfunctionalequation |