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

Abstract EN

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.