참고문헌
- J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.
-
C. Baak, D.-H. Boo and Th.M. Rassias, Generalized additive mapping in Banach modules and isomorphisms between
$c^{\ast}$ -algebras, J. Math. Anal. Appl. 314 (2006), 150-161. https://doi.org/10.1016/j.jmaa.2005.03.099 - P. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002.
-
c V.A. Faizev, Th.M. Rassias and P.K. Sahoo, The space of
$({\psi},{\gamma})$ -additive mappings on semigroups, Trans. Amer. Math. Soc. 354 (11) (2002), 4455-4472. https://doi.org/10.1090/S0002-9947-02-03036-2 - 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
- H. Haruki and Th.M. Rassias, New generalizations of Jensen's functional, Proc. Amer. Math. Soc. 123 (1995), 495-503.
- 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
- D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Mathematicae 44 (1992), 125-153. https://doi.org/10.1007/BF01830975
- D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.
-
G. Isac and 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 - K. Jun and Y. Lee, A generalization of the Hyers-Ulam-Rassias stabilitity of the Pexiderized quadratic equations, J. Math. Anal. Appl. 297 (2004), 70-86. https://doi.org/10.1016/j.jmaa.2004.04.009
- S.-M. Jung and Th.M. Rassias, Ulam's problem for approximate homomorphisms in connection with Bernoulli's differential equation, Applied Mathematics and Computation 187(2007), 223-227. https://doi.org/10.1016/j.amc.2006.08.120
- S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press Inc., Palm Harbor, Florida, 2001.
- R.V. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249-266.
- M.S. Moslehian and Th.M. Rassias, Stability of functional equations in non-Archimedean spaces, Applicable Analysis and Discrete Mathematics 1 (2007), 325-334. https://doi.org/10.2298/AADM0702325M
- A. Najati, Hyers-Ulam stability of an n-Apollonius type quadratic mapping, Bull.Belgian Math. Soc. Simon-Stevin. 14, (2007), 755-774.
- A. Najati, On the stability of a quartic functional equation, J. Math. Anal. Appl. 340 (2008), 569-574. https://doi.org/10.1016/j.jmaa.2007.08.048
- A. Najati and M.B. Moghimi, Stability of a functional equation deriving from quadratic andadditive functions in quasi-Banach spaces, J. Math. Anal. Appl. 337 (2008), 399-415. https://doi.org/10.1016/j.jmaa.2007.03.104
- A. Najati and C. Park, Hyers-Ulam-Rassias, stability of homonorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation, J. Math. Anal. Appl. 335 (2007), 763-778. https://doi.org/10.1016/j.jmaa.2007.02.009
- C. Park, On the stability of linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), 711-720. https://doi.org/10.1016/S0022-247X(02)00386-4
- C. Park, Y. Cho and M. Han, Stability of functional inequalities associated with Jordonvon Neumann type additive functional equations, J. Inequal. Appl. (2007), Art. ID 41820.
-
C.-G. Park and Th.M. Rassias, On a generalized Trif's mapping in Banach modules over a
$c^{\ast}$ -algebra, J. Korean Math. Soc. 43 (2) (2006), 323-356. https://doi.org/10.4134/JKMS.2006.43.2.323 - C. Park and Th.M. Rassias, Isometric additive mappings in quasi-Banach spaces, Nonlinear Functional Analysis and APPLICATIONS, 12 (3) (2007), 377-385.
-
C. Park and Th.M. Rassias, Homomorphisms and derivations in proper
$JCQ^{\ast}$ -triples, J. Math. Anal. Appl. 337. (2008), 1404-1414. https://doi.org/10.1016/j.jmaa.2007.04.063 - J.M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982) 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
- 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, On the stability of functional equations and a problem of Ulam, Acta Applicandae Mathematicae 62 (1) (2000), 23-130. https://doi.org/10.1023/A:1006499223572
- Th.M. Rassias and J. Tabor, What is left of Hyers-Ulam stabilirty? Journal of Natural Geometry, 1 (1992), 65-69.
- Th.M.Rassias (ed.), Topics in Mathematical Analysis, A Volume dedicated to the Memory of A.L. Cauchy, World Scientific Publishing Co., Singapore, New Jersey, London, 1989.
- Th.M. Rassias and J. Tabor (eds.) , Stability of Mappings of Hyers-Ulam Type, Hadronic Press Inc., Florida, 1994.
- Th.M.Rassias (ed.) , Functional Equations and Inequations and Inequalities, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000.
- Th.M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers Co., Dordrecht, Boston, London, 2003.
- S.M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.