DOI QR코드

DOI QR Code

GENERALIZED ULAM-HYERS STABILITY OF C*-TERNARY ALGEBRA 3-HOMOMORPHISMS FOR A FUNCTIONAL EQUATION

  • Bae, Jae-Hyeong (Graduate School of Education, Kyung Hee University) ;
  • Park, Won-Gil (Department of Mathematics Education, Mokwon University)
  • 투고 : 2010.12.15
  • 심사 : 2011.02.15
  • 발행 : 2011.06.30

초록

In this paper, we investigate the Ulam-Hyers stability of $C^{\star}$-ternary algebra 3-homomorphisms for the functional equation $$f(x_1+x_2,y_1+y_2,z_1+z_2)=\;\displaystyle\sum_{1{\leq}i,j,k{\leq}2}\;f(x_i,y_j,z_k)$$ in $C^{\star}$-ternary algebras.

키워드

참고문헌

  1. V. Abramov, R. Kerner and B. Le Roy, Hypersymmetry: a $\mathbb{Z}_3$-graded general- ization of supersymmetry, J. Math. Phys. 38 (1997), 1650-1669. https://doi.org/10.1063/1.531821
  2. M. Amyari and M.S. Moslehian, Approximately ternary semigroup homomor- phisms, Lett. Math. Phys. 77 (2006), 1-9. https://doi.org/10.1007/s11005-005-0042-6
  3. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Jpn. 2 (1950), 64. https://doi.org/10.2969/jmsj/00210064
  4. J.-H. Bae and W.-G. Park , Generalized Jensen's functional equations and approximate algebra homomorphisms, Bull. Korean Math. Soc. 39 (2002), 401- 410. https://doi.org/10.4134/BKMS.2002.39.3.401
  5. J.-H. Bae and W.-G. Park , On the generalized Hyers-Ulam-Rassias stability in Banach modules over a $C^{\ast}$-algebra, J. Math. Anal. Appl. 294 (2004), 196-205. https://doi.org/10.1016/j.jmaa.2004.02.009
  6. J.-H. Bae and W.-G. Park , Approximate bi-homomorphisms and bi-derivations in $C^{\ast}$-ternary algebras, Bull. Korean Math. Soc. 47 (2010), 195-209. https://doi.org/10.4134/BKMS.2010.47.1.195
  7. D.G. Bourgin, Classes of transformations and bordering transformations, Bull. Am. Math. Soc. 57 (1951), 223. https://doi.org/10.1090/S0002-9904-1951-09511-7
  8. A. Cayley, On the 34 concomitants of the ternary cubic, Am. J. Math. 4 (1881), 1-15. https://doi.org/10.2307/2369145
  9. Y. L. Daletskii and L. Takhtajan, Leibniz and Lie algebra structures for Nambu algebras, Lett. Math. Phys. 39 (1997), 127-141. https://doi.org/10.1023/A:1007316732705
  10. Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431-434. https://doi.org/10.1155/S016117129100056X
  11. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  12. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  13. M. Kapranov, I.M. Gelfand and A. Zelevinskii, Discriminants, Resultants and Multidimensional Determinants, Birkhauser, Berlin, 1994.
  14. R. Kerner, The cubic chessboard: Geometry and physics, Classical Quantum Gravity 14 (1997), A203-A225. https://doi.org/10.1088/0264-9381/14/1A/017
  15. R. Kerner, Ternary algebraic structures and their applications in physics, Proc. BTLP 23rd Int. Colloquium on Group Theoretical Methods in Physics, 2000 (arXiv:math-ph/0011023).
  16. M. S. Moslehian, Almost derivations on $C^{\ast}$-ternary rings, Bull. Belgian Math. Soc.-Simon Stevin 14 (2007), 135-142.
  17. C. Park, Isomorphisms between $C^{\ast}$-ternary algebras, J. Math. Phys. 47 (2006), 103512. https://doi.org/10.1063/1.2359576
  18. W.-G. Park and J.-H. Bae, On a bi-quadratic functional equation and its sta- bility, Nonlinear Anal. 62 (2005), 643-654. https://doi.org/10.1016/j.na.2005.03.075
  19. W.-G. Park and J.-H. Bae, On the solution of a multi-additive functional equa- tion and its stability, J. Appl. Math. & Computing 22 (2006), 517-522.
  20. A. Prastaro, Geometry of PDEs and Mechanics, World Scientific, River Edge, NJ, 1996: MR1412798 (98e:58182).
  21. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
  22. Th. M. Rassias and P. Semrl, On the behaviour of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993. https://doi.org/10.1090/S0002-9939-1992-1059634-1
  23. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York, 1960.
  24. L. Vainerman and R. Kerner, On special classes of n-algebras, J. Math. Phys. 37 (1996), 2553-2565. https://doi.org/10.1063/1.531526
  25. H. Zettl, A characterization of ternary rings of operators, Adv. Math. 48 (1983), 117-143. https://doi.org/10.1016/0001-8708(83)90083-X