Generalized Jordan derivations on Frechet algebras
Abstract
Jordan derivations on Frechet algebras.
Moreover, we prove the generalized Hyers-Ulam-Rassias stability and
superstability of generalized Jordan derivations on Frechet algebras.
An important issue is so that we do not assume that the Frechet algebra is unital.
Full Text:
PDFReferences
%---------------------------------------------------------
bibitem{Aoki}
T. Aoki,
{em On the stability of the linear transformation in Banach spaces},
J. Math. Soc. Japan. 2 (1950), 64-66.
%---------------------------------------------------------
bibitem{Badora}
R. Badora,
{em On approximate derivations},
Math. Inequal. Appl. 9 (2006), 167-173.
%---------------------------------------------------------
bibitem{Bavand}
M. Bavand Savadkouhi, M. E. Gordji, J. M. Rassias and N. Ghobadipour,
{em Approximate ternary Jordan derivations on Banach ternary algebras},
J. Math. Phys. 50 (2009), 9 pages.
%---------------------------------------------------------
bibitem{Cze}
S. Czerwik,
{em Stability of functional equations of Ulam-Hyers-Rassias type},
Hadronic Press, Florida, 2003.
%---------------------------------------------------------
bibitem{Ebadian}
A. Ebadian, N. Ghobadipor and M. E. Gordji,
{em A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C*-ternary algebras},
J. Math. Phys. 51, 1 (2010), 10 pages, DOI:10.1063/1.3496391.
%---------------------------------------------------------
bibitem{Ebadian22}
A. Ebadian, A. Najati and M. E. Gordji,
{em On approximate additve-quartic and quadratic-cubic functional equations in two variables on Abelian groups},
Results. Math. 58, (2010), 39-53, DOI:10.1007/s00025-010-0018-4.
%---------------------------------------------------------
bibitem{Ebad2}
A. Ebadian, I. Nikoufar, and M. E. Gordji,
{em Nearly $(theta_1, theta_2, theta_3, phi)$-derivations on Hilbert C*-modules},
Int. J. Geom. Methods. Mod. Phys., vol. 9, no. 3, 1250019, (2012), 12 pages.
%---------------------------------------------------------
bibitem{Gordji2}
M. Eshaghi Gordji and N. Ghobadipor,
{em stability of $(alpha,beta,gamma)$-derivation on Lie C*-algebras},
Int. J. Geom. Methods Mod. Physics,
Vol. 7, No. 7 (2010), 1-10, DOI:10.1142/S0219887810004737.
%-------------------------------
bibitem{Es3}
M. Eshaghi Gordji and N. Ghobadipour,
{em Nearly generalized Jordan derivations},
Math. Slovaca, Vol. 61, No. 1, (2011), 55-62, DOI: 10.2478/s12175-010-0059-x.
%---------------------------------------------------------
bibitem{Gordji3}
M. Eshaghi Gordji, M. Ramezani, A. Ebadian and C. Park,
{em Quadratic double centralizers and quadratic multipliers},
Ann. Univ. Ferrara (2011), 57:27-38, DOI:10.1007/s11565-011-0115-7
%---------------------------------------------------------
bibitem{Moslehian}
M. S. Moslehian,
{em Hyers-Ulam-Rassias stability of generalized derivations},
Int. J. Math. Sci. vol. (2006), 1-8, Article ID 93942.
%---------------------------------------------------------
bibitem{Park}
C. Park,
{em Homomorphisms between Poisson JC$^*$-algebras},
Bull. Braz. Math. Soc. 36 (2005), 79-97.
%---------------------------------------------------------
bibitem{Park22}
C. Park,
{em Lie $*$-homomorphisms between Lie C*-algebras and Lie $*$-derivations on Lie C*-algebras},
J. Math. Anal. Appl. 293 (2004), no. 2, 419-434.
%---------------------------------------------------------
bibitem{Gajda}
Z. Gajda,
{em On stability of additive mappings },
Int. J. Math. Sci. 14 (1991), 431-434.
%---------------------------------------------------------
bibitem{Gavruta}
P. Gavruta,
{em A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings},
J. Math. Anal. Appl. 184 (1994), 431-436.
%---------------------------------------------------------
bibitem{Gavruta22}
P. Gavruta and L. Gavruta,
{em A new method for the generalized Hyers-Ulam-Rassias stability},
Int. J. Nonlinear. Anal. Appl. 1 (2010), no. 2, 11-18.
%---------------------------------------------------------
bibitem{Hyers}
D. H. Hyers,
{em On the stability of the linear functional equation},
Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
%---------------------------------------------------------
bibitem{Hyers22}
D. H. Hyers, G. Issac and Th. M. Rassias,
{em Stability of functional equations in several variables},
Birkhauser, Basel, 1998.
%---------------------------------------------------------
bibitem{Khodaei}
H. Khodaei and Th. M. Rassias,
{em Approximately generalized additive functions in several variables},
Int. J. Nonlinear. Anal. Appl., 1, (2010), no. 1, 22-41.
bibitem{Miura}
%---------------------------------------------------------
T. Miura, S. E. Takahashi and G. Hirasawa,
{em Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras},
J. Inequal. Appl. 1, (2004), 435-441.
%---------------------------------------------------------
bibitem{Rassias}
Th. M. Rassias,
{em On the stability of the linear mapping in Banach spaces},
Proc. Amer. Math. Soc. 72 (1978), 297-300.
%---------------------------------------------------------
bibitem{Rassias22}
Th. M. Rassias,
{em Problem 16; 2, Report of the 27th International symposium on functional equations},
Aequationes Math. vol. 39, (1990), 292-293; 309.
%---------------------------------------------------------
bibitem{Rassias33}
Th. M. Rassias and P. Semrl,
{em On the behaviour of mappings which do not satisfy Hyers-Ulam stability},
Proc. Amer. Math. Soc. 114 (1992), 989-993.
%---------------------------------------------------------
bibitem{Ulam}
S. M. Ulam,
{em A collection of mathematical problems},
Interscience Tracts in Pure and Applied Mathematics, Interscience Publisher, New York, 1960.
Refbacks
- There are currently no refbacks.