Taiwanese Journal of Mathematics

STABILITY OF $n$-JORDAN $*$-DERIVATIONS IN $C^{*}$-ALGEBRAS AND $JC^{*}$-ALGEBRAS

Shahram Ghaffary Ghaleh and Khatereh Ghasemi

Full-text: Open access

Abstract

In this paper, we investigate superstability and the Hyers-Ulam stability of $n$-Jordan $*$-derivations in $C^{*}$-algebras and $JC^{*}$-algebras for the generalized Jensen-type functional equation $$r f(\frac{a+b}{r}) + r f(\frac{a-b}{r}) = 2 f(a).$$

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1791-1802.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406797

Digital Object Identifier
doi:10.11650/twjm/1500406797

Mathematical Reviews number (MathSciNet)
MR2970685

Zentralblatt MATH identifier
1267.39023

Subjects
Primary: 17C65: Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 39B52: Equations for functions with more general domains and/or ranges 39B72: Systems of functional equations and inequalities 46L05: General theory of $C^*$-algebras

Keywords
$n$-Jordan $*$-derivation $C^{*}$-algebra $JC^{*}$-algebra Hyers-Ulam stability

Citation

Ghaleh, Shahram Ghaffary; Ghasemi, Khatereh. STABILITY OF $n$-JORDAN $*$-DERIVATIONS IN $C^{*}$-ALGEBRAS AND $JC^{*}$-ALGEBRAS. Taiwanese J. Math. 16 (2012), no. 5, 1791--1802. doi:10.11650/twjm/1500406797. https://projecteuclid.org/euclid.twjm/1500406797


Export citation

References

  • T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66.
  • B. Baak, D. Boo and Th. M. Rassias, Generalized additive mapping in Banach modules and isomorphisms between $C^{*}$-algebras, J. Math. Anal. Appl., 314 (2006), 150-161.
  • S. Czerwik, Function Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, USA, 2002.
  • M. Eshaghi Gordji, Nearly $n$-Jordan derivations, (preprint).
  • M. Eshaghi Gordji, On approximate $n$-ring homomorphisms and $n$-ring derivations, Nonlinear Funct. Anal. Appl., (to appear).
  • M. Eshaghi Gordji, Nearly Ring Homomorphisms and Nearly Ring Derivations on Non-Archimedean Banach Algebras, Abstr. Appl. Anal., 2010 (2010), 1-12.
  • M. Eshaghi Gordji and Z. Alizadeh, Stability and superstability of ring homomorphisms on nonarchimedean banach algebras, Abstract and Applied Analysis, 2011, Article ID 123656, 2011, 10 pages.
  • M. Eshaghi Gordji, A. Bodaghi and I. A. Alias, On the stability of quadratic double centralizers and quadratic multipliers: a fixed point approach, Journal of Inequalities and Applications, 2011, Article ID 957541, 2011, 12 pages.
  • M. Eshaghi Gordji, M. B. Ghaemi, S. Kaboli Gharetapeh, S. Shams and A. Ebadian, On the stability of $J^{*}$-derivations, Journal of Geometry and Physics, 60 (2010), 454-459.
  • M. Eshaghi Gordji, N. Ghobadipour and C. Park, Jordan $*$-homomorphisms on $C^{*}$-algebras, Operators and Matrices, 5 (2011), 541-551.
  • A. Ebadian, Approximately $n$-Jordan derivations: a fixed point approach, preprint.
  • S. Hejazian, M. Mirzavaziri and M. S. Moslehian, $n$-Homomorphisms, Bull. Iranian Math. Soc., 31 (2005), 13-23.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224.
  • D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications, Boston, MA, USA, 1998.
  • D. H., Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992), 125-153.
  • G. Isac and Th. M. Rassias, On The Hyers-Ulam Stability of $\psi$-additive mapping, J. Approx. Theorym 72 (1993), 131-137.
  • G. Isac and Th. M. Rassias, Stability of $\psi$-additive mapping, J. Math. Sci., 19 (1996), 219-228.
  • S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Harmonic Press, Palm Harbor, FL, USA, 2001.
  • T. Miura, S.-E. Takahasi and G. Hirasawa, Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras, Journal of Inequalities and Applications, 2005 (2005), 435-441.
  • C. Park, Homomorphisms between Poisson $JC^{*}$-algebras, Bull. Braz. Math. Soc., 36 (2005), 79-97.
  • C. Park, Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras, Bull. Sci. Math., 132 (2008), 87-96.
  • C. Park and J. M. Rassias, Stability of the Jensen-type functional equation in $C^{*}$-algebras: a fixed point approach, Abstract and Applied Analysis, 2009, Article ID 360432, 17 pages, 2009.
  • Th. M. Rassias and P. Semrl, On the behavior of mapping which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc., 114, (1992), 989-993.
  • Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.
  • C. Park, The problem of S. M. Ulam for approximately multiplicative mapping, J. Math. Anal. Appl., 246 (2000), 352-378.
  • S. M. Ulam, Problems in Modern Mathematics, Chapter VI. Science ed. Wily, New York, 1940.