Abstract
In this work, we introduce quadratic Jordan *-derivations on real C*-algebras and real JC*-algebras and prove the Hyers–Ulam stability of Jordan *-derivations and of quadratic Jordan *-derivations on real C*-algebras and real JC*-algebras. We also establish the superstability of such derivations on real C*-algebras and real JC*-algebras by using a fixed point theorem.
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