Generalized Hyers-Ulam stability of derivations on Lie * C -algebras
DOI:
https://doi.org/10.24297/jap.v3i1.2087Keywords:
-derivation,, (m,n) -Cauchy-Jensen additive functional equation, Lie * C -algebra, generalized Hyers-Ulam stabilityAbstract
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Abellanas, L. and Alonso, L. 1975. A general setting for Casimir invariants, J. Math. Phys. 16, 1580-1584.
Aoki, T. 1950. On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2, 64-66.
Asgari, Gh., Cho, Y.J., Lee, Y.W. and Gordji, M.E. 2013. Fixed points and stability of functional equations in fuzzy
ternary Banach algebras, J. Inq. Appl. 2013:166 doi:10,1186/1029-242X-2013-166.
C a dariu, L. and Radu, V. 2003. Fixed points and the stability of Jensen’s functional equation, J. Ineq. Pure Appl. Math. 4, No.1, Art. 4.
C a dariu, L. and Radu, V. 2004. On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Berichte 346, 43-52.
Cho, Y.J., Saadati, R. and Vahidi, J. 2012. Approximation of homomorphisms and derivations on non-Archimedean Lie * C -algebras via fixed point method, Dis. Dyn. Nat. Soc. 2012, Article ID 373904, pp 9.
Dias, J.B. and Margolis, B. 1968. A fixed point theorem of the alternative for contrations on a generalized complete metric space, Bull. Amer. Math. Soc. 74, 305-309.
Ga vruta, P. 1994. A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184(1994), 431-436.
Gordji, M.E. and Ghobadipour, N. 2010. Stability ofderivation on Lie * C -algebras, Int. J. Geom.
Methods in Modern Phys. 7, 1093-1102.
Hyers, D.H. 1941. On the stability of the linear functional equation, Proc. Natl. Acad. Sci. 27, 222-224.
Jacobson, N. 1979. Lie Algebras, Dover, New York.
Kim, S.S., Rassias, J.M., Cho, Y.J. and Kim, S.H. 2013. Stability of n -Lie homomorphisms and Jordan n -Lie
homomorphisms on n -Lie algebras, J. Math. Phys. 54, 53501.
Mirmostaface, A.K. 2012. Pertubation of generalized derivations in fuzzy Menger normed algebras, Fuzzy sets and systems, 195, 109-117.
Najati, A., Park, C. and Lee, J.R. 2009. Homomorphisms and derivations in * C -ternary algebras, Abstract Appl. Anal. 2009, Artical ID 612392.
Novotny, P. and Hrivnak, J. 2008. On derivations of Lie algebras and corresponding invariant functions,
J. Geom. Phys. 58, 208-217.
Park, C. 2005. Homomorphisms between Lie * JC -algebras and Cauchy-Rassias stability of Lie * JC -algebra
derivations, J. Lie Theory 15, 393-414.
Park, C. 2005. Homomorphisms between Poissin * JC -algebras, Bull. Brazil. Math. Soc. 36, 79-97.
Park, C. and Rassias, J.M. 2009. Stability of the Jensen-type functional equation in C*-algebras: a fixed point
approach, Abs. Appl. Anal. Art. ID 360432.
Popovych, R., Boyko, V., Nesterenko, M. and Lutfullin, M. 2003. Realizations of real low-dimensional Lie algebras, J. Phys. A36. 7337-7360.
Rand, D., Winternitz, P. and Zassenhaus, H. 1988. On the identification of Lie algebra given by its structure constants I. Direct decompositions, Levi decompositions and nil radicals, Linear Algebra Appl. 109, 197-246.
Rassias, J.M. and Kim, H.M. 2008. Approximate homomorphisms and derivations between * C -ternary algebras, J. Math. Phys. 49. 063507.
Rassias, J.M., Jun, K.W. and Kim, H.M. 2011. Approximate (m,n) -Cauchy-Jensen additive mappings in * C
-algebras, Acta Math. Sinica, 27, 1907-1922.
Rassias, Th.M. 1978. On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, 297-300.
Ulam, S.M. 1940. Problems in Modern Mathematics, Science Editions, John Wiley & Sons, New York, USA.
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