JORDAN *-DERIVATIONS AND QUADRATIC JORDAN *-DERIVATIONS ON REAL C*-ALGEBRAS AND REAL JC*-ALGEBRAS

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.