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GENERALIZED HYERS–ULAM STABILITY OF ADDITIVE FUNCTIONAL EQUATIONS

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In this paper, we obtain the general solution and the generalized Hyers- Ulam stability theorem for an additive functional equation af(x + y) + 2f(x/2+ y) + 2f(x +y/2) = (a + 3)[f(x) + f(y)] for any fixed integer a.

Abstract

In this paper, we obtain the general solution and the generalized Hyers- Ulam stability theorem for an additive functional equation af(x + y) + 2f(x/2+ y) + 2f(x +y/2) = (a + 3)[f(x) + f(y)] for any fixed integer a.

참고문헌 (11)

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  4. D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci.U.S.A, 27, pp.222~224 (1941)
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  6. A. Najati, "Stability of homomorphisms on JB-triples associated to a Cauchy-Jensentype functional equation", J. Math. Ineq, 1, pp.83~103 (2007)
  7. J. M. Rassias, "Generalized Hyers-Ulam stability for general additive functionalequations in quasi- -normed spaces", J. Math. Anal. Appl, 356, pp.302~309 (2009)
  8. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer.Math. Soc, 72, pp.297~300 (1978)
  9. Th. M. Rassias, "The stability of mappings and related topics, In ‘Report on the 27thISFE’", Aequationes. Math, 39, pp.292~293 (1990)
  10. Th. M. Rassias, "On the behaviour of mappings which do not satisfy Hyers-Ulam-Rassias stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
  11. S.M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ

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