DOI QR코드

DOI QR Code

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.

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

Cited by

  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