Acknowledgement
Supported by : National Research Foundation of Korea(NRF)
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
- J.-H. Bae and W.-G. Park, On the solution of a bi-Jensen functional equation and its stability, Bull. Korean Math. Soc. 43 (2006), 499-507. https://doi.org/10.4134/BKMS.2006.43.3.499
- P. GAvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. and Appl. 184 (1994,) 431-436. https://doi.org/10.1006/jmaa.1994.1211
- D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
- K.-W. Jun and H.-M. Kim, Remarks on the stability of additive functional equation, Bull. Korean Math. Soc. 38 (2001), 679-687.
- K.-W. Jun, Y.-H. Lee and Y.-S. Cho, On the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation, Abstract Appl. Anal. (2007), ID 35351, 15 pages.
- K.-W. Jun, Y.-H. Lee and J.-H. Oh, On the Rassias stability of a bi-Jensen functional equation, J. Math. Ineq. 2 (2008), 363-375.
- K.-W. Jun, I.-S. Jung and Y.-H. Lee, Stability of a bi-Jensen functional equation, to appear.
- 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
- G.-H. Kim and Y.-H. Lee, Hyers-Ulam stability of a bi-Jensen functional equation on a punctured domain, J. Ineq. Appl. 2010 (2010), Art. 476249, 15 pages.
- H.-M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl. 324 (2006), 358-372. https://doi.org/10.1016/j.jmaa.2005.11.053
- Y.-H. Lee and K.-W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc. 128 (2000), 1361-1369. https://doi.org/10.1090/S0002-9939-99-05156-4
- 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), 289-296. https://doi.org/10.1007/s00010-007-2892-8
-
C.-G. Park, Linear functional equations in Banach modules over a
$C^{\ast}$ -algebra, Acta Appl. Math. 77 (2003), 125-161. https://doi.org/10.1023/A:1024014026789 - W.-G. Park and J.-H. Bae, On a Cauchy-Jensen functional equation and its stability, J. Math. Anal. Appl. 323 (2006), 634-643. https://doi.org/10.1016/j.jmaa.2005.09.028
- 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
- S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1968, p. 63.