Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation | Zendy

M‎. ‎Eshaghi Gordji | Zendy; Mohammad Bagher Ghaemi | Zendy; Gwang Hui Kim | Zendy; Badrkhan Alizadeh | Zendy

Open Access

Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation

Author(s) -

M‎. ‎Eshaghi Gordji,

Mohammad Bagher Ghaemi,

Gwang Hui Kim,

Badrkhan Alizadeh

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/726020

Subject(s) - mathematics , automorphism , functional equation , cauchy distribution , fixed point theorem , pure mathematics , stability (learning theory) , fixed point , mathematical analysis , partial differential equation , computer science , machine learning

Let be an algebra, and let , be ring automorphisms of . An additivemapping ∶→ is called a (,)-derivation if ()=()()+()() for all ,∈. Moreover, an additive mapping ∶→ is said to be a generalized (,)-derivation if there exists a (,)-derivation ∶→ such that ()=()()+()() for all ,∈. In this paper, we investigate the superstability of generalized (,)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation

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