References
- Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis, Vol. 1, Colloq. Publ. vol. 48, Amer. Math. Soc. Providence, 2000.
- C. Borelli and G.L. Forti, On a general Hyers-Ulam stability result, Internat. J. Math. Math. Sci. 18 (1995), 229-236. https://doi.org/10.1155/S0161171295000287
- I. Chang and H. Kim, On the Hyers-Ulam stability of quadratic functional equations, J. Inequal. Pure and Appl. Math. Vol. 3 (2002), Article 33, 12pages.
- H. Chu and S. Yoo, On the stability of an additive set-valued functional equation, J. Chungcheong Math. Soc. 27 (2014), no. 3, 455-467. https://doi.org/10.14403/jcms.2014.27.3.455
- 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
- G. Han, Fuzzy stability for a class of quadratic functional equations, J. Chungcheong Math. Soc. 27 (2014), no. 1, 123-132. https://doi.org/10.14403/jcms.2014.27.1.123
- 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
- C. Kim and C. Shin, The generalized Hyers-Ulam stability of quadratic functional equation with an involution in non-Archimedean spaces, J. Chungcheong Math. Soc. 27 (2014), no. 2, 261-269. https://doi.org/10.14403/jcms.2014.27.2.261
- S. Lee, J. Bae and W. Park, On the Hyers-Ulam stability of an additive functional inequality, J. Chungcheong Math. Soc. 26 (2013), no. 4, 671-681. https://doi.org/10.14403/jcms.2013.26.4.671
- S. Lee, Generalized Hyers-Ulam stability of refined quadratic functional equation, preprint.
- 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
- J.M. Rassias, On the stability of the non-linear Euler-Lagrange functional equation, Chinese J. Math. 20 (1992), no. 2, 185-190.
-
J.M. Rassias and H. Kim, Generalized Hyers-Ulam stability for additive functional equations in quasi-
${\beta}$ -normed spaces, J. Math. Anal. Appl. 356 (2009), 302-309. https://doi.org/10.1016/j.jmaa.2009.03.005 - S. Rolewicz, Metric linear spaces, Reidel/PWN-Polish Sci. Publ. Dordrecht, 1984.
- 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, Problems in Modern Mathematics, Chap. VI, Wiley, New York, (1960).
- A. Zivari-Kazempour and M. Eshaghi Gordji, Generalized Hyers-Ulam Stabilities of an Euler-Lagrange-Rassias quadratic functional equation, Asian European J. Math. 5 (2012), Doi:10.1142/S1793557112500143.