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The generalized cubic functional equation and the stability of cubic Jordan $$*$$ ∗ -derivations

The generalized cubic functional equation and the stability of cubic Jordan $$*$$ ∗ -derivations In the current work, we obtain the general solution of the following generalized cubic functional equation $$\begin{aligned}&f(x+my)+f(x-my)\\&\quad =2\left( 2\cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(x)-\frac{1}{2}\left( \cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(2x)\\&\qquad +m^2\{f(x+y)+f(x-y)\} \end{aligned}$$ f ( x + m y ) + f ( x - m y ) = 2 2 cos m π 2 + m 2 - 1 f ( x ) - 1 2 cos m π 2 + m 2 - 1 f ( 2 x ) + m 2 { f ( x + y ) + f ( x - y ) } for an integer $$m \ge 1$$ m ≥ 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 $$C^*$$ C ∗ -algebras and $$JC^*$$ J C ∗ -algebras. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

The generalized cubic functional equation and the stability of cubic Jordan $$*$$ ∗ -derivations

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-013-0185-9
Publisher site
See Article on Publisher Site

Abstract

In the current work, we obtain the general solution of the following generalized cubic functional equation $$\begin{aligned}&f(x+my)+f(x-my)\\&\quad =2\left( 2\cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(x)-\frac{1}{2}\left( \cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(2x)\\&\qquad +m^2\{f(x+y)+f(x-y)\} \end{aligned}$$ f ( x + m y ) + f ( x - m y ) = 2 2 cos m π 2 + m 2 - 1 f ( x ) - 1 2 cos m π 2 + m 2 - 1 f ( 2 x ) + m 2 { f ( x + y ) + f ( x - y ) } for an integer $$m \ge 1$$ m ≥ 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 $$C^*$$ C ∗ -algebras and $$JC^*$$ J C ∗ -algebras.

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Jul 13, 2013

References

  • Approximate multipliers and approximate double centralizers: a fixed point approach
    Bodaghi, A; Eshaghi Gordji, M; Paykan, K
  • Fixed points and the stability of quadratic functional equations
    Cădariu, L; Radu, V
  • On the stability of the Cauchy functional equation: a fixed point approach
    Cădariu, L; Radu, V
  • On the stability of the quadratic mapping in normed spaces
    Czerwik, S
  • A fixed point theorem of the alternative for contractions on a generalized complete metric space
    Diaz, JB; Margolis, B
  • A fixed point approach to the stability of double Jordan centralizers and Jordan multipliers on Banach algebras
    Eshaghi Gordji, M; Bodaghi, A; Park, C
  • Approximately $$J^*$$ J ∗ -homomorphisms: a fixed point approach
    Eshaghi Gordji, M; Najati, A
  • On the stability of the linear functional equation
    Hyers, DH
  • Stability of Functional Equations in Several Variables
    Hyers, DH; Isac, G; Rassias, ThM
  • On the stability of a generalized cubic functional equation
    Koh, H; Kang, D
  • Hyers–Ulam–Rassias stability of a cubic functional equation
    Najati, A
  • The generalized Hyers–Ulam–Rassias stability stability of a cubic functional equation
    Najati, A
  • The generalized Hyers–Ulam–Russias stability of a cubic functional equation
    Jun, KW; Kim, HM
  • On the Hyers–Ulam–Rassias stability of a general cubic functional equation
    Jun, KW; Kim, HM
  • Homomorphisms between Poisson $$JC^*$$ J C ∗ -algebras
    Park, C
  • On the stability of the linear mapping in Banach spaces
    Rassias, ThM
  • Stability of a cubic fuctional equation in fuzzy normed space
    Ravi, K; Rassias, JM; Narasimman, P
  • The stability of the cubic functional equation in various spaces
    Saadati, R; Vaezpour, SM; Park, C
  • Problems in Modern Mathematics, Chapter VI
    Ulam, SM