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THE STABILITY OF A MIXED TYPE FUNCTIONAL INEQUALITY WITH THE FIXED POINT ALTERNATIVE

  • 발행 : 2004.04.01

초록

In this note, by using the fixed point alternative, we investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional inequality which is either cubic or quadratic: $\parallel$8f(x-3y) + 24f(x+y) + f(8y) -8〔f(x+3y) + 3f(x-y) + 2f(2y)〕$\parallel$$\leq$$\varphi$(x,y).

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참고문헌

  1. Functional Equations in Serveral Variables J.Aczel;J.Dhombres
  2. Proc. Amer. Math. Soc, v.80 The stability of the cosine equation J.Baker https://doi.org/10.2307/2043730
  3. Aequationes Math. v.27 Remarks on the stability of functional equations P.W.Cholewa https://doi.org/10.1007/BF02192660
  4. Abh. Math. v.62 On the stability of the quadratic mapping in normed spaces S.Czerwik https://doi.org/10.1007/BF02941618
  5. Trans. Amer. Math. Soc. v.364 no.11 The space of (φ,γ)-additive mappings on semigroups V.A.Faiziev;Th.M.Rassias;P.K.Sahoo
  6. 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
  7. Proc. Natl. Acad. Sci. v.27 On the stability of the linear fuctional equation D.H.Hyers https://doi.org/10.1073/pnas.27.4.222
  8. Stability of Functional Equations in Several Variables D.H.Hyers;G.Isac;Th.M.Rassias
  9. Proc. Amer. Math. Soc. v.126 On the asymptoticity aspect of Hyers-Ulam stability of mappings https://doi.org/10.1090/S0002-9939-98-04060-X
  10. Aequationes Math. v.44 Approximate homomorphisms D.H.Hyers;Th.M.Rassias https://doi.org/10.1007/BF01830975
  11. J. Math. Anal. Appl. v.274 no.2 The generalized Hyers-Ulam-Rassias stability of a cubic functional equation K.W.Jun;H.M.Kim https://doi.org/10.1016/S0022-247X(02)00415-8
  12. J. Math. Anal. Appl. v.222 On the Hyers-Ulam stability of the functional equations that have the quadratic property S.M.Jung https://doi.org/10.1006/jmaa.1998.5916
  13. J. Math. Anal. Appl. v.274 no.2 On the stability of the functional equation f(x+y+xy)=f(x)+f(y)+xf(y)+yf(x)+yf(x) Y.S.Jung;K.H.Park https://doi.org/10.1016/S0022-247X(02)00328-1
  14. Results Math. v.27 Quadratic functional equation and inner product spaces Pl.Kannappan https://doi.org/10.1007/BF03322841
  15. Bull. Amer. Math. Soc. v.126 no.74 A fixed point theorem of the alternative for contractions on a generalized complete metric space B.Margolis;J.B.Diaz
  16. Seminar on Fixed Point Theory Cluj-Napoca v.Ⅳ The fixed point alternative and the stability of functional equations V.Radu
  17. Glas. Mat. v.36 no.1 Solution of the Ulam stability problem for cubic mappings J.M.Rassias
  18. J. Math. Anal. Appl. v.276 On the Ulam stability of the mixed type mappings on restricted domains https://doi.org/10.1016/S0022-247X(02)00439-0
  19. Proc. Amer. Math. Soc, v.72 On the stability of the linear mapping in Banach spaces Th. M. Rassias https://doi.org/10.2307/2042795
  20. J. Math. Anal. Appl. v.251 On the stability of functional equations in Banach spaces https://doi.org/10.1006/jmaa.2000.7046
  21. Acta Math. Appl. v.62 On the stability of functional equations and a problem of Ulam https://doi.org/10.1023/A:1006499223572
  22. Functional Equations and inequalities Th.M.Rassias(ed.)
  23. Journal of Natural Geometry v.1 What is left of Hyers-Ulam stability
  24. Stability of mappings of Hyers-Ulam type
  25. Proc. Amer. Math. Soc, v.114 On the behavior of mappings which does not satisfy Hyers-Ulam stability Th.M.Rasslas;P.Semrl https://doi.org/10.2307/2159617
  26. Rend. Sem. Mat. Fis. Milano v.53 Proprieta locali e approssimazione di operatori F.Skof https://doi.org/10.1007/BF02924890
  27. Science Problems in Modern Mathematics S.M.Ulam