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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/726020 |