Stability and Superstability of Generalized (๐, ๐)-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation
Let ๐ด be an algebra, and let ๐, ๐ be ring automorphisms of ๐ด. An additive mapping ๐ปโถ๐ดโ๐ด is called a (๐,๐)-derivation if ๐ป(๐ฅ๐ฆ)=๐ป(๐ฅ)๐(๐ฆ)+๐(๐ฅ)๐ป(๐ฆ) for all ๐ฅ,๐ฆโ๐ด. Moreover, an additive mapping ๐นโถ๐ดโ๐ด is said to be a generalized (๐,๐)-derivation if there exists a (๐,๐)-derivation ๐ปโถ๐ดโ๐ด such that ๐น(๐ฅ๐ฆ)=๐น(๐ฅ...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2011-01-01
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Series: | Journal of Applied Mathematics |
Online Access: | http://dx.doi.org/10.1155/2011/726020 |
Summary: | Let ๐ด be an algebra, and let ๐, ๐ be ring automorphisms of ๐ด. An additive
mapping ๐ปโถ๐ดโ๐ด is called a (๐,๐)-derivation if ๐ป(๐ฅ๐ฆ)=๐ป(๐ฅ)๐(๐ฆ)+๐(๐ฅ)๐ป(๐ฆ) for all ๐ฅ,๐ฆโ๐ด. Moreover, an additive mapping ๐นโถ๐ดโ๐ด is said to be a generalized (๐,๐)-derivation if there exists a (๐,๐)-derivation ๐ปโถ๐ดโ๐ด such that ๐น(๐ฅ๐ฆ)=๐น(๐ฅ)๐(๐ฆ)+๐(๐ฅ)๐ป(๐ฆ) for all ๐ฅ,๐ฆโ๐ด. In this paper, we investigate the superstability of generalized (๐,๐)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchyโs functional equation. |
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ISSN: | 1110-757X 1687-0042 |