Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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GENERALIZED QUADRATIC FUNCTIONAL EQUATION WITH SEVERAL VARIABLES AND ITS HYERS-ULAM STABILITY

  • Kim, Hark-Mahn (Department of Mathematics, Chungnam National University) ;
  • Liang, Hong Mei (Department of Mathematics, Chungnam National University)
  • Received : 2015.12.22
  • Accepted : 2016.01.15
  • Published : 2016.02.15
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Abstract

In this paper, we introduce a generalized quadratic functional equation with several variables and then investigate its generalized Hyers-Ulam stability in normed spaces.

Keywords

References

  1. 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
  2. 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
  3. Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431-434. https://doi.org/10.1155/S016117129100056X
  4. 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
  5. 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
  6. S. -M. Jung, A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl. 2007 (2007), Article ID 57064, 9 pages.
  7. S. -M. Jung and Z. -H. Lee, A fixed point approach to the stability of quadratic functional equation with involution, Fixed Point Theory Appl. 2008(2008), Article ID 732086, 11 pages.
  8. B. Margolis and J. B. Diaz, 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
  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
  10. J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. 108 (1984), 445-446.
  11. J. M. Rassias, On the stability of the non-linear Euler-Lagrange functional equation, Chinese J. Math. 20 (1992), 185-190.
  12. V. Radu, The fixed point altenative and the stability of functional equations, Sem. Fixed Point Theory 4 (2003), no. 1, 91-96.
  13. F. Skof, Local properties and approximations of operators, Rend. Sem. Math. Fis. Mil. 53 (1983), 113-129. https://doi.org/10.1007/BF02924890
  14. S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Wiley, New York, 1960.
  15. 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.

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