ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 59, Issue 2, pp 235–250

The generalized cubic functional equation and the stability of cubic Jordan \(*\)-derivations

  • Abasalt Bodaghi
  • Seyed Mohsen Moosavi
  • Hamidreza Rahimi
Article

DOI: 10.1007/s11565-013-0185-9

Cite this article as:
Bodaghi, A., Moosavi, S.M. & Rahimi, H. Ann Univ Ferrara (2013) 59: 235. doi:10.1007/s11565-013-0185-9

Abstract

In the current work, we obtain the general solution of the following generalized cubic functional equation
$$\begin{aligned}&f(x+my)+f(x-my)\\&\quad =2\left( 2\cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(x)-\frac{1}{2}\left( \cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(2x)\\&\qquad +m^2\{f(x+y)+f(x-y)\} \end{aligned}$$
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.

Keywords

Banach algebra Cubic derivation Cubic functional equation Hyers–Ulam stability Superstability 

Mathematics Subject Classification (2010)

39B52 39B72 46L05 47B47 

Copyright information

© Università degli Studi di Ferrara 2013

Authors and Affiliations

  • Abasalt Bodaghi
    • 1
  • Seyed Mohsen Moosavi
    • 2
  • Hamidreza Rahimi
    • 3
  1. 1.Department of Mathematics, Garmsar BranchIslamic Azad UniversityGarmsarIran
  2. 2.Department of Basic SciencesEyvanekey Institute of Higher EducationGarmsarIran
  3. 3.Department of Mathematics, Central Tehran BranchIslamic Azad UniversityTehranIran

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