In the current work, we obtain the general solution of the following generalized cubic functional equation
for an integer \(m \ge 1\). We prove the Hyers–Ulam stability and the superstability for this cubic functional equation by the directed method and a fixed point approach. We also employ the mentioned functional equation to establish the stability of cubic Jordan \(*\)-derivations on \(C^*\)-algebras and \(JC^*\)-algebras.
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The authors express their sincere thanks to the reviewers for the careful and detailed reading of the manuscript and very helpful suggestions that improved the manuscript substantially.
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Bodaghi, A., Moosavi, S.M. & Rahimi, H. The generalized cubic functional equation and the stability of cubic Jordan \(*\)-derivations. Ann Univ Ferrara 59, 235–250 (2013). https://doi.org/10.1007/s11565-013-0185-9
- Banach algebra
- Cubic derivation
- Cubic functional equation
- Hyers–Ulam stability
Mathematics Subject Classification (2010)