참고문헌
- J. Aczel & J. Dhombres: Functional Equations in Several Variables. Cambridge Univ. Press, 1989.
-
C. Baak & M.S. Moslehian:
$\theta$ -derivations on JB*-triples. Bull. Braz. Math. Soc. 38 (2007), no. 1, 115-127. https://doi.org/10.1007/s00574-007-0039-0 - J. Baker: The stability of the cosine equation. Proc. Amer. Math. Soc. 80 (1980), 411-416. https://doi.org/10.1090/S0002-9939-1980-0580995-3
- P.W. Cholewa: Remarks on the stability of functional equations. Aequationes Math. 27 (1984), 76-86. https://doi.org/10.1007/BF02192660
- S. Czerwik: On the stability of the quadratic mapping in normed spaces. Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64. https://doi.org/10.1007/BF02941618
- 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
- P. Gavruta: An answer to a question of John M. Rassias concerning the stability of Cauchy equation. in: Advances in Equations and Inequalities, in: Hadronic Math. Ser. (1999), 67-71.
- M.S. Moslehian: Hyers-Ulam-Rassias stability of generalized derivations. Internat. J. Math. & Math. Sci. 2006 (2006), 1-8.
- O. Hatori & 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
- D.H. Hyers, G. Isac & Th.M. Rassias: On the asymptoticity aspect of Hyers-Ulam stability of mappings. Proc. Amer. Math. Soc. 126 (1968), no. 2, 425-430.
- B.E. Johnson: Continuity of generalized homomorphisms. Bull. London Math. Soc. 19 (1987), 67-71. https://doi.org/10.1112/blms/19.1.67
- S.-M. Jung: On the Hyers-Ulam stability of the functional equations that have the quadratic property. J. Math. Anal. Appl. 222 (1998), 126-137. https://doi.org/10.1006/jmaa.1998.5916
- S.-M. Jung: Hyers-Ulam-Rassias stability of Jensen's equation and its application. Proc. Amer. Math. Soc. 126 (1998), 3137-3143. https://doi.org/10.1090/S0002-9939-98-04680-2
- S.-M. Jung: Hyers-Ulam-Rassias Stability of Functional equations in Mathematical Analy- sis. Hadronic Press, Inc., Palm Harbor, Florida, 2001.
- Y.-S. Jung: On the stability of the functional equation f(x+y-xy)+xf(y)+yf(x) = f(x) + f(y). Math. Inequal. & Appl. 7 (2004), no. 1, 79-85.
- Y.-S. Jung & I.-S. Chang: On approximately higher ring derivations. J. Math. Anal. Appl. 343 (2008), no. 2, 636-643. https://doi.org/10.1016/j.jmaa.2008.01.083
- T. Miura, G. Hirasawa & 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
- J.M. Rassias: On Approximation of Approximately Linear Mappings by Linear Map- pings. J. Funct. Anal. USA 46 (1982), 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
- Pl. Kannappan: Quadratic functional equation and inner product spaces. Results Math. 27 (1995), 368-372. https://doi.org/10.1007/BF03322841
- 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
- Th.M. Rassias(Ed.): "Functional Equations and inequalities". Kluwer Academic, Dordrecht, Boston, London, 2000.
- Th.M. Rassias: "Stability of mappings of Hyers-Ulam type". Hadronic Press, Inc., Florida, 1994.
- 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
- F. Skof: Local properties and approximations of operators. Rend. Sem. Mat. Milano 53 (1983), 113-129. https://doi.org/10.1007/BF02924890
- S.M. Ulam: A Collection of Mathematical Problems. Interscience Publ., New York, 1960.