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STABILITY OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION WITH JENSEN TYPE

LEE, YOUNG-WHAN    (Department of Computer and Information Security, Daejeon University  );
  • 초록

    In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.


  • 주제어

    hyers-ulam-rassias stability .   quadratic functional equation .   Popoviciu functional equation.  

  • 참고문헌 (26)

    1. Y. W. Lee, The stability of derivations on Banach algebras, Bull. Inst. Math. Acad. Sinica 28 (2000), 113-116 
    2. G. L. Forti, Hyers- Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), 146-190 
    3. Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's Equation, J. Math. Anal. Appl. 238 (1999), 305-315 
    4. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436 
    5. D. H. Hyers, On the stability of the linear functional equation, Proc, Natl. Acad. Sci. USA 21 (1941), 222-224 
    6. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston/Basel/Berlin, 1998 
    7. D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153 
    8. K. W. Jun, G. H. Kim, and Y. W. Lee, Stability of generalized gamma and beta functional equations, Aequationes Math. 60 (2000), 15-24 
    9. S. M. Jung, Huers-Ulam-Rassias stability of functional equations, Dynam. Systems Appl. 6 (1997), 541-566 
    10. S. M. Jung, Hyers- Uuim-Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), 3137-3143 
    11. S. M. Jung, On the Hyers- Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), 126-137 
    12. S. M. Jung, On the Hyers- Ulam-Rassias stability of a quadratic functional equation, J. Math. Anal. Appl. 232 (1999), 384-393 
    13. G. H. Kim, On the stability of the quadratic mapping in normal space, IJMMs 25 (2001), no. 4, 217-229 
    14. E. H. Lee, Y. W. Lee, and S. H. Park, Stability of a Jensen type functional Equations, J. Appl. Math. Comput. 10 (2002), no. 1-2, 283-295 
    15. S. H. Lee and Y. W. Lee, Stability of a Popoviciu functional Equations, Nonlinear Funct. Anal. Appl. 7 (2002), no. 3, 413-429 
    16. Y. W. Lee, On the stability of a quadratic Jensen type functional Equation, J. Math. Anal. Appl. 270 (2002), 590-601 
    17. Th. M. Rassias, On a problem of S. M Ulam and the asymptotic stability of the Cauchy functional equation with applications, General Inequalities 7, MFO, Oberwolfach, Birkhiiuser Verlag, Basel ISNM 123 (1997), 297-309 
    18. Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23-130 
    19. Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284 
    20. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300 
    21. Th. M. Rassias, On the stability of the quadratic functional equation and its applications, Studia, Univ. Babes-Bolyai XLIII 3 (1998), 89-124 
    22. Th. M. Rassias, The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), 352-378 
    23. Th. M. Rassias and P. Semrl, On the behavior of mapping that do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993 
    24. T. Trif, Hyers-Ulam-Rassias stability of a quadratic functional equation, Bull. Korean Math. Soc. 40 (2003), 253-267     
    25. S. M. Ulam, Problems in Modern Mathematics, Proc. Chap. VI. Wiley. New York, 1964 
    26. T. Trif, Hyers- Ulam-Rassias stability of a Jensen type functional Equation, J. Math. Anal. Appl. 250 (2000), 579-588 
  • 이 논문을 인용한 문헌 (2)

    1. 2006. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 43(3): 499~507     
    2. 2010. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 47(1): 195~209     

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