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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

journal of applied mathematics

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