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

M. Eshaghi Gordji, M. B. Ghaemi, G. H. Kim and Badrkhan Alizadeh

Journal of Applied Mathematics, 2011, vol. 2011, issue 1

Abstract: 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.

Date: 2011
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https://doi.org/10.1155/2011/726020

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