Stability and superstability of generalized (θ,φ)-derivations in non-archimedean algebras: Fixed point theorem via the additive cauchy functional equation

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 (x y) = 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 (x y) = 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 cauchys functional equation. copyright © 2011 m. eshaghi gordji et al.