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

[摘要] LetAbe an algebra, and letθ,ϕbe ring automorphisms ofA. An additivemappingH:A→Ais called a(θ,ϕ)-derivation ifH(xy)=H(x)θ(y)+ϕ(x)H(y)for allx,y∈A. Moreover, an additive mappingF:A→Ais said to be a generalized(θ,ϕ)-derivation if there exists a(θ,ϕ)-derivationH:A→Asuch thatF(xy)=F(x)θ(y)+ϕ(x)H(y)for allx,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.

[学科分类] 应用数学