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Stability of a cubic functional equation on groups

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Abstract

In this note we will find out the general solution and investigatethe generalized Hyers-Ulam-Rassias stability for the cubicfunctional equation f(3x+y)+f(3x-y) =3f(x+y)+3f(x-y)+48f(x) onabelian groups.

참고문헌 (14)

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  3. "newblock Remarks on the stability offunctional equations", 27(1-2), pp.76~ (1984)
  4. "newblock On the stability of thequadratic mapping in normed spaces", 62, pp.59~ (1992)
  5. "newblock Characterizations of inner product spaces" (1986)
  6. "newblock A generalization of the Hyers-Ulam-Rassias stability ofapproximately additive mappings", 184(3), pp.431~ (1994)
  7. "newblock On the stability of the linear functional equation", 27, pp.222~ (1941)
  8. "newblock Stability of functional equations in several variables,newblock Birkh" (1998)
  9. "Jordan and J. Von Neumann newblock On inner products in linear newblock Ann. of Math. 36", pp.719~ (1935)
  10. "newblock On the Hyers-Ulam stability ofthe functional equations that have the quadratic property,newblock", 222(1), pp.126~137 (1998)
  11. "newblock On the stabilityof the functional equation ff(x+y+xy)=f(x)+f(y)+xf(y)+yf(x)", pp.659~ (2002)
  12. "newblock Quadratic functionalequation and inner product spaces", 27(3-4), pp.368~372 (1995)
  13. "newblock On the stability of the linearmapping in Banach spaces", 72(2), pp.297~ (1978)
  14. "newblock Problems in modern mathematics", vi (1964)

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