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A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON

  • Jun, Kil-Woung (Department of Mathematics Chungnam National University) ;
  • Jung, Soon-Mo (Mathematics Section College of Science and Technology Hong-Ik University) ;
  • Lee, Yang-Hi (Department of Mathematics Education Kongju National University)
  • Published : 2004.05.01

Abstract

We prove the Hyers-Ulam-Rassias stability of the Davison functional equation f($\chi$y) + f($\chi$ + y) = f($\chi$y + $\chi$) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

Keywords

References

  1. Aequationes Math. v.20 191R1.Remark W.Benz
  2. Aequationes Math. v.46 On approximate solutions of Pexider equation J.Chmielinskii;J.Tabor https://doi.org/10.1007/BF01834004
  3. Aequationes Math. v.20 191R1. Probem T.M.K.Davison
  4. J. Math. Anal. Appl. v.184 A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings P.Gavruta https://doi.org/10.1006/jmaa.1994.1211
  5. Aequationes Math. v.60 A functional equations of Davison ad its generalization R.Girgensohn;K.Lajko https://doi.org/10.1007/s000100050148
  6. Proc. Natl. Acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D.H.Hyers https://doi.org/10.1073/pnas.27.4.222
  7. Stability of Functional Equations in Several Variables D.H.Hyer;G.Isac;Th.M.Rassias
  8. Dynam. Sys. Appl. v.6 Hyers-Ulam-Rassias stability of functional equations S.M.Jung
  9. J. Math. Anal. Appl. v.238 Hyers-Ulam stability of an equation od Davison S.M.Jung;P.K.Sahoo https://doi.org/10.1006/jmaa.1999.6545
  10. Kyungpook Math. J. v.40 On the Hyers-Ulam stability of functiona equation of Davison S.M.Jung;P.K.Sahoo
  11. J. Math. Anal. Appl. v.246 A Generalization of the Hyers-Ulam-Rassias Stability of Pexider Equation Y.H.Lee;K.W.Jun https://doi.org/10.1006/jmaa.2000.6832
  12. J. Korean Math. Soc. v.37 A Note on the Hyers-Ulam-Rassias Stability of Pexider Equation Y.H.Lee;K.W.Jun
  13. Proc. Amer. Math. Soc. v.128 On the Stability of Approximately Additive Mappings Y.H.Lee;K.W.Jun https://doi.org/10.1090/S0002-9939-99-05156-4
  14. Proc. Amer. Math. Soc. v.72 On the stabiligy of the linear mapping in Banach spaces Th.M.Rassias https://doi.org/10.2307/2042795
  15. J. Math. Anal. Appl. v.158 On a modified Hyers-Ulam sequence Th.M.Rassias https://doi.org/10.1016/0022-247X(91)90270-A
  16. J. Math. Anal. Appl. v.173 On the Hyers-Ulam stability of linear mappings Th.M.Rassias;P.Semrl https://doi.org/10.1006/jmaa.1993.1070
  17. Problems in Modern Mathematics(Science ed.) S.M.Ulam

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  1. Ulam–Hyers–Rassias stability problem for several kinds of mappings vol.24, pp.4, 2013, https://doi.org/10.1007/s13370-012-0078-6
  2. Hyers–Ulam stability of a functional equation with several parameters vol.27, pp.7-8, 2016, https://doi.org/10.1007/s13370-016-0403-6
  3. HYERS-ULAM STABILITY OF MAPPINGS FROM A RING A INTO AN A-BIMODULE vol.28, pp.4, 2013, https://doi.org/10.4134/CKMS.2013.28.4.767