DOI QR코드

DOI QR Code

On the Generalized Hyers-Ulam-Rassias Stability of Higher Ring Derivations

Park, Kyoo-Hong;Jung, Yong-Soo

  • 투고 : 2008.02.20
  • 심사 : 2008.09.02
  • 발행 : 2009.03.31

초록

We establish the generalized Hyers-Ulam-Rassias stability of higher ring derivations. Furthermore, we use the superstability of higher ring derivations to obtain approximately higher linear derivations mapping into the Jacobson radical under some conditions.

키워드

higher ring derivation;approximately higher ring derivation;stability

참고문헌

  1. R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl., 276(2)(2002), 589-597. https://doi.org/10.1016/S0022-247X(02)00293-7
  2. R. Badora, On approximate derivations, Math. Inequal. Appl., 9(1)(2006), 167-173.
  3. D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J., 16(1949), 385-397. https://doi.org/10.1215/S0012-7094-49-01639-7
  4. Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14(1991), 431-434. https://doi.org/10.1155/S016117129100056X
  5. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  6. O. Hatori and J. Wada, Ring derivations on semi-simple commutative Banach algebras, Tokyo J. Math., 15(1992), 223-229. https://doi.org/10.3836/tjm/1270130262
  7. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  8. K.-W. Jun and Y.-W. Lee, The image of a continuous strong higher derivation is contained in the radical, Bull. Korean Math. Soc., 33(1996), 229-233.
  9. T. Miura, G. Hirasawa and S.-E. Takahasi, A perturbation of ring derivations on Banach algebras, J. Math. Anal. Appl., 319(2006), 522-530. https://doi.org/10.1016/j.jmaa.2005.06.060
  10. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  11. I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann., 129(1955), 260-264. https://doi.org/10.1007/BF01362370
  12. S. M. Ulam, A Collection of Mathematical Problems, Interscience Publ., New York, 1960.

피인용 문헌

  1. A General System of Nonlinear Functional Equations in Non-Archimedean Spaces vol.53, pp.3, 2013, https://doi.org/10.5666/KMJ.2009.49.1.067