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ON THE STABILITY OF FUNCTIONAL EQUATIONS IN n-VARIABLES AND ITS APPLICATIONS

KIM, GWANG-HUI    (Department of Mathematics Kangnam University  );
  • 초록

    In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$ , where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.


  • 주제어

    functional equation, gamma .   beta and G-function .   Hyers-Ulam stability .   Hyers-Ulam-Rassias stability.  

  • 참고문헌 (27)

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    5. R. Ger, Superstability is not natural, Rocznik Nauk.-Dydakt. Prace Mat. 159 (1993), 109-123 
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    9. G. Isac and Th. M. Rassias, On the Hyers-Ulam stability of A-additive mappings, J. Approx. Theory 72 (1993), 131-137 
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    11. S.-M. Jung, On the general Hyers-Ulam stability of gamma functional equation, Bull. Korean Math. Soc. 34 (1997), 437-446 
    12. S.-M. Jung, On the modified Hyers-Ulam-Rassias stability of the functional equation for gamma function, Mathematica 39 (1997), 233-237 
    13. S.-M. Jung, On the stability of gamma functional equation, Results Math. 33 (1998), 306-309 
    14. G. H. Kim, On the stability of generalized Gamma functional equation, Internat. J. Math. & Math. Sci. 23 (2000), 513-520 
    15. G. H. Kim, A generalization of the Hyers-Ulam-Rassias stability of the Beta functional equation, Publ. Math. Debrecen 59 (2001), 111-119 
    16. G. H. Kim, A generalization of Hyers-Ulam-Rassias stability of a G-functional equation, Math. Inequal. Appl., to appear 
    17. G. H. Kim, Y.W. Lee, The stability of the beta functional equation, Studia Univ. 'Babes-Bolyai', Mathematica 40 (2000), 89-96 
    18. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300 
    19. Th. M. Rassias, On the modified Hyers-Ulam sequence, J. Math. Anal. Appl. 158 (1991), 106-113 
    20. Th. M. Rassias, On the stability of functional equations in Banach space, J. Math. Anal. Appl. 251 (2000), 264-284 
    21. Th. M. Rassias (ed.), Functional Equations and Inequalities, Kluwer Academic Publishers, Dordrecht, 2000 
    22. Th. M. Rassias (ed.), Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 2003 
    23. Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993 
    24. Th. M. Rassias and J. Tabor, Stability of Mappings of Hyers-Ulam Type, Hadronic Press Inc., Florida, 1994 
    25. T. Trip, On the stability of a general gamma-type functional equation, Publ. Math. Debrecen 60 (2002), 47-62 
    26. S. M. Ulam, Problems in Modern Mathematics, Chap. VI , Science editions, Wiley, New York, 1964 
    27. Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23-130 
  • 이 논문을 인용한 문헌 (1)

    1. 2008. "" Communications of the Korean Mathematical Society = 대한수학회논문집, 23(3): 371~376     

 저자의 다른 논문

  • Kim, Gwang-Hui (15)

    1. 1997 "Approximate Jordan mappings on noncommutative Banach algebras" Communications of the Korean Mathematical Society = 대한수학회논문집 12 (1): 69~73    
    2. 2000 "THE STABILITY OF THE GENERALIZED FORM FOR THE GAMMA FUNCTIONAL EQUATION" Communications of the Korean Mathematical Society = 대한수학회논문집 15 (1): 45~50    
    3. 2000 "ON STABILITY OF THE EQUATION - g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$" The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A 7 (3): 1017~1027    
    4. 2001 "MODIFIED HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS WITH SQUARE-SYMMETRIC OPERATION" Communications of the Korean Mathematical Society = 대한수학회논문집 16 (2): 211~223    
    5. 2001 "HYERS-ULAM STABILITY OF HOMOGENEOUS FUNCTIONAL EQUATIONS" The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A 8 (2): 569~580    
    6. 2002 "STABILITY OF THE G-FUNCTIONAL EQUATION" The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A 9 (2): 837~844    
    7. 2004 "ON THE STABILITY OF A BETA TYPE FUNCTIONAL EQUATIONS" Journal of applied mathematics & computing 14 (1): 429~445    
    8. 2005 "ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS" Communications of the Korean Mathematical Society = 대한수학회논문집 20 (1): 93~106    
    9. 2007 "ON THE STABILITY OF THE COSINE TYPE FUNCTIONAL EQUATION" Journal of the Korean Society of Mathematical Education. 한국수학교육학회지. Series B, Pure and applied mathematics 14 (1): 7~14    
    10. 2007 "THE STABILITY OF THE GENERALIZED SINE FUNCTIONAL EQUATIONS III" 충청수학회지 = Journal of the Chungcheong Mathematical Society 20 (4): 465~476    

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