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Stability of the Quadratic Equation of Pexider Type

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Abstract

We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik, and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic functional equation of Pexider type,f 1 (x +y) + f2(x -y) =f 3(x) +f 4(y), for a large class of functions.

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References

  1. J. Aczél andJ. Dhombres,Functional Equations in Several Variables. Cambridge Univ. Press 1989.

  2. C. Borelli andG. L. Forti, On a general Hyers-Ulam stability result.Internat. J. Math. Math. Sci. 18 (1995), 229–236.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. W. Cholewa, Remarks on the stability of functional equations.Aequationes Math. 27 (1984), 76–86.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Czerwik, On the stability of the quadratic mapping in normed spaces.Abh. Math. Sem. Univ. Hamburg 62 (1992), 59–64.

    Article  MATH  MathSciNet  Google Scholar 

  5. -, The stability of the quadratic functional equation. In:Stability of Mappings of Hyers-Ulam Type (edited by Th. M. Rassias and J. Tabor), Hadronic Press 1994, pp. 81–91.

  6. G. L. Forti, Hyers-Ulam stability of functional equations in several variables.Aequationes Math. 50 (1995), 143–190.

    Article  MATH  MathSciNet  Google Scholar 

  7. Z. Gajda, On stability of additive mappings.Internat. J. Math. Math. Sci. 14 (1991), 431–434.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Găvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings.J. Math. Anal. Appl. 184 (1994), 431–436.

    Article  MATH  MathSciNet  Google Scholar 

  9. D. H. Hyers, On the stability of the linear functional equation.Proc. Nat. Acad. Sci. U.S. A. 27 (1941), 222–224.

    Article  MathSciNet  Google Scholar 

  10. D. H. Hyers,G. Isac andTh. M. Rassias,Stability of Functional Equations in Several Variables. Birkhäuser 1998.

  11. D. H. Hyers andTh. M. Rassias, Approximate homomorphisms.Aequationes Math. 44 (1992), 125–153.

    Article  MATH  MathSciNet  Google Scholar 

  12. S.-M. Jung, On the Hyers-Ulam-Rassias stability of approximately additive mappings.J. Math. Anal. Appl. 204 (1996), 221–226.

    Article  MATH  MathSciNet  Google Scholar 

  13. —, Hyers-Ulam-Rassias stability of functional equations.Dynamic Systems and Applications 6 (1997), 541–566.

    MATH  MathSciNet  Google Scholar 

  14. J. M. Rassias, On the stability of the Euler-Lagrange functional equation.C. R. Acad. Bulgare Sci. 45 (1992), 17–20.

    MATH  MathSciNet  Google Scholar 

  15. Th. M. Rassias, On the stability of the linear mapping in Banach spaces.Proc. Amer. Math. Soc. 72 (1978), 297–300.

    Article  MATH  MathSciNet  Google Scholar 

  16. -, On the stability of the quadratic functional equation and its applications. To appear.

  17. F. Skof, Proprietá locali e approssimazione di operatori.Rend. Sem. Mat. Fis. Milano 53 (1983), 113–129.

    Article  MATH  MathSciNet  Google Scholar 

  18. S. M. Ulam,Problems in Modern Mathematics. Chapter VI. Science Editions, Wiley 1964.

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  1. Mathematics Section, College of Science & Technology, Hong-Ik University, 339-701, Chochiwon, Korea

    Soon-Mo Jung

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Correspondence to Soon-Mo Jung.

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Jung, SM. Stability of the Quadratic Equation of Pexider Type. Abh.Math.Semin.Univ.Hambg. 70, 175–190 (2000). https://doi.org/10.1007/BF02940912

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