참고문헌
- 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
- C. Borelli and G. L. Forti, On a general Hyers-Ulam stability result, Internat. J. Math. Math. Sci. 18 (1995), no. 2, 229-236. https://doi.org/10.1155/S0161171295000287
- D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223-237. https://doi.org/10.1090/S0002-9904-1951-09511-7
- L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 4, 7 pp.
- L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara, Ser. Mat.-Inform. 41 (2003), no. 1, 25-48.
- L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Iteration theory (ECIT '02), 43-52, Grazer Math. Ber., 346, Karl-Franzens-Univ. Graz, Graz, 2004.
- S. Czerwik, The stability of the quadratic functional equation, Stability of mappings of Hyers-Ulam type, 8191, Hadronic Press Collect. Orig. Artic., Hadronic Press, Palm Harbor, FL, 1994.
- H. G. Dales and M. S. Moslehian, Stability of mappings on multi-normed spaces, Glasg. Math. J. 49 (2007), no. 2, 321-332. https://doi.org/10.1017/S0017089507003552
- H. G. Dales and M. E. Polyakov, Multi-normed spaces and multi-Banach algebras, arxiv:1112.5148v2 (2012).
- J. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
- M. Eshaghi Gordji and S. Abbaszadeh, Stability of Cauchy-Jensen inequalities in fuzzy Banach spaces, Appl. Comput. Math. 11 (2012), no. 1, 27-36.
- M. Eshaghi Gordji and H. Khodaei, Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear Anal. 71 (2009), no. 11, 5629-5643. https://doi.org/10.1016/j.na.2009.04.052
-
M. Eshaghi Gordji, H. Khodaei, and Th. M. Rassias, Fixed points and stability for quadratic mappings in
${\beta}$ -normed left Banach modules on Banach algebras, Results Math. 61 (2012), no. 3-4, 393-400. https://doi.org/10.1007/s00025-011-0123-z - M. Eshaghi Gordji and F. Moradlou, Approximate Jordan derivations on Hilbert C*-modules, Fixed Point Theory, (to appear).
- M. Eshaghi Gordji, A. Najati, and A. Ebadian, Stability and superstability of Jordan homomorphisms and Jordan derivations on Banach algebras and C*-algebras: a fixed point approach, Acta Math. Sci. Ser. B Engl. Ed. 31 (2011), no. 5, 1911-1922.
- M. Eshaghi Gordji and M. Bavand Savadkouhi, Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces, Appl. Math. Lett. 23 (2010), no. 10, 1198-1202. https://doi.org/10.1016/j.aml.2010.05.011
- M. Eshaghi Gordji and M. Bavand Savadkouhi, Stability of cubic and quartic functional equations in non-Archimedean spaces, Acta Appl. Math. 110 (2010), no. 3, 1321-1329. https://doi.org/10.1007/s10440-009-9512-7
- P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. https://doi.org/10.1006/jmaa.1994.1211
- 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
- S.-M. Jung and J. M. Rassias, A fixed point approach to the stability of a functional equation of the spiral of Theodorus, Fixed Point Theory and Applications, 2008 (2008), Art. ID: 945010, 7 pp. https://doi.org/10.1155/2008/945010
- H.-M. Kim and J. M. Rassias, Generalization of Ulam stability problem for Euler-Lagrange quadratic mappings, J. Math. Anal. Appl. 336 (2007), no. 1, 277-296. https://doi.org/10.1016/j.jmaa.2007.02.075
- Y.-S. Lee and S.-Y. Chung, Stability of an Euler-Lagrange-Rassias equation in the spaces of generalized functions, Appl. Math. Lett., 21 (2008), no. 7, 694-700. https://doi.org/10.1016/j.aml.2007.07.022
- L. Maligranda, A result of Tosio Aoki about a generalization of Hyers-Ulam stability of additive functions - a question of priority, Aequationes Math. 75 (2008), no. 3, 289-296. https://doi.org/10.1007/s00010-007-2892-8
- F. Moradlou, A. Najati, and H. Vaezi, Stability of homomorphisms and derivations on C*-ternary rings associated to an Euler-Lagrange type additive mapping, Results Math. 55 (2009), no. 3-4, 469-486. https://doi.org/10.1007/s00025-009-0410-0
- F. Moradlou, H. Vaezi, and G. Z. Eskandani, Hyers-Ulam-Rassias stability of a quadratic and additive functional equation in quasi-Banach spaces, Mediterr. J. Math. 6 (2009), no. 2, 233-248. https://doi.org/10.1007/s00009-009-0007-6
- F. Moradlou, H. Vaezi, and C. Park, Fixed points and stability of an additive functional equation of n-Apollonius type in C*-algebras, Abstr. Appl. Anal. 2008 (2008), Article ID 672618, 13 pages, 2008. doi:10.1155/2008/672618.
- M. S. Moslehian, Approximate C*-ternary ring homomorphisms, Bull. Braz. Math. Soc. 38 (2007), no. 4, 611-622. https://doi.org/10.1007/s00574-007-0064-z
- M. S. Moslehian, K. Nikodem, and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, J. Math. Anal. Appl. 355 (2009), no. 2, 717-724. https://doi.org/10.1016/j.jmaa.2009.02.017
- C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), no. 2, 711-720. https://doi.org/10.1016/S0022-247X(02)00386-4
- C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory Appl. 2007 (2007), Art. ID 50175, 15 pp.
- C. Park, Stability of an Euler-Lagrange-Rassias type additive mapping, Int. J. Appl. Math. Stat. 7 (2007), 101-111.
- C. Park, Hyers-Ulam-Rassias stability of a generalized Apollonius-Jensen type additive mapping and isomorphisms between C*-algebras, Math. Nachr. 281 (2008), no. 3, 402-411. https://doi.org/10.1002/mana.200510611
- C. Park and Th. M. Rassias, Hyers-Ulam stability of a generalized Apollonius type quadratic mapping, J. Math. Anal. Appl. 322 (2006), no. 1, 371-381. https://doi.org/10.1016/j.jmaa.2005.09.027
- A. Pietrzyk, Stability of the Euler-Lagrange-Rassias functional equation, Demonstratio Mathematica 39 (2006), no. 3, 523-530.
- V. Radu, The fixed point alternative and stability of functional equations, Fixed Point Theory 4 (2003), no. 1, 91-96.
- J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), no. 1, 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
- J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. 108 (1984), no. 4, 445-446.
- J. M. Rassias and M. J. Rassias, Refined Ulam stability for Euler-Lagrange type mappings in Hilbert spaces, Int. J. Appl. Math. Stat. 7 (2007), 126-132.
- Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
- Th. M. Rassias, The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), no. 2, 352-378. https://doi.org/10.1006/jmaa.2000.6788
- Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284. https://doi.org/10.1006/jmaa.2000.7046
- F. Skof, Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. https://doi.org/10.1007/BF02924890
- S. M. Ulam, A Collection of Mathematical Problems, Interscience Publ. New York, 1960.
- T. Zhou Xu, J. M. Rassias, and W. Xin Xu, Generalized Ulam-Hyers stability of a general mixed AQCQ-functional equation in multi-Banach spaces: a fixed point approach, Eur. J. Pure Appl. Math. 3 (2010), no. 6, 1032-1047.
피인용 문헌
- GENERALIZED HYERS-ULAM-RASSIAS STABILITY FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES vol.50, pp.6, 2013, https://doi.org/10.4134/BKMS.2013.50.6.2061