References
- T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc., Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
- R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), 589-597. https://doi.org/10.1016/S0022-247X(02)00293-7
- R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006), 167-173.
- F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, Heidelberg and Berlin, (1973).
- 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
- M. Bresar and J. Vukman, On the left derivation and related mappings, Proc. Amer. Math. Soc., 10 (1990), 7-16.
- D. Han and F. Wei, Generalized Jordan left derivations on semiprime algebras, Monatsh. Math. Soc., 161 (2010), 77-83. https://doi.org/10.1007/s00605-009-0116-0
- 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
- 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
- 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
-
G. Isac, Th.M. Rassias, On the Hyers-Ulam stability of
$\psi$ -additive mappings, J. Approx. Theory, 72 (1993), 131-137. https://doi.org/10.1006/jath.1993.1010 - B.E. Johnson, Continuity of derivations on commutative Banach algebras, Amer. J. Math., 91 (1969), 1-10. https://doi.org/10.2307/2373262
- T. Miura, G. Hirasawa and S.-E. Takahasi, A pertubation of ring derivations on Banach algebras, J. Math. Anal. Appl., 319 (2006), 522-530. https://doi.org/10.1016/j.jmaa.2005.06.060
- Y.H. Lee and K.W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., 128 (1999), 1361-1369. https://doi.org/10.1090/S0002-9939-99-05156-4
- M.S. Moslehian, Hyers-Ulam-Rassias stability of generalized derivations, Int. J. Math. Math. Sci., (2006), Art. ID 93942, 8 pp.
- C. Park, Linear derivations on Banach algebras, Nonlinear. Funct. Anal. Appl., 9 (2004), 359-368.
- 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
- P. Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integr. Equat. Oper. Theory 18 (1994), 118-122. https://doi.org/10.1007/BF01225216
- I.M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann, 129 (1955), 260-264. https://doi.org/10.1007/BF01362370
- M.P. Thomas, The image of a derivation is contained in the radical, Ann. of Math., 128 (1988), 435-460. https://doi.org/10.2307/1971432
- S.M. Ulam, Problems in Modern Mathematics, Chap. VI, Science ed., Wiley, New York., (1960).