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ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS

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

    In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$ . As a consequence in the cases ${\varphi}(x) := x+p:= x+1$ , we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.


  • 주제어

    Functional equation .   Hyers-Ulam stability .   Hyers-Ulam­Rassias stability .   G-function .   double gamma function.  

  • 참고문헌 (15)

    1. E. W. Barnes, The theory of the double gamma function, Proc. Roy. Soc. London Ser. A 196 (1901), 265-388 
    2. E. W. Barnes, The theory of the G-function, Quart. J. Math. 31 (1899), 264-314 
    3. J. Choi and H. M. Srivastava, Certain classes of series involving the Zeta func- tion, J. Math. Anal. Appl. 231 (1999), 91-117 
    4. P. Gavruta, A Generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436 
    5. R. Ger, Superstability is not natural, Roczik Nauk.-Dydakt. Prace Mat. 159 (1993), 109-123 
    6. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224 
    7. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equation in Several Variables, Birkhauser, Basel, 1998 
    8. S. M. Jung, On the modified Hyers-Ulam-Rassias stability of the functional equation for gamma function, Mathematica 39(62) (1997), no. 2, 233-237 
    9. S. M. Jung, On the stability of G-functional equation, Results Math. 33 (1998), 306-309 
    10. K. W. Jun, G. H. Kim and Y. W. Lee, Stability of generalized gamma and beta functional equations, Aequationes Math. 60 (2000), 15-24 
    11. G. H. Kim, On the stability of generalized Gamma functional equation, Internat. J. Math. Math. Sci. 23 (2000), 513-520 
    12. G. H. Kim, Stability of the G-functional equation, J. Appl. Math. Comput. 23 (2000), 513-520 
    13. G. H. Kim, The stability of generalized Gamma functional equation, Nonlinear Studies. 7(1) (2000), 92-96 
    14. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300 
    15. S. M. Ulam, 'Problems in Modern Mathematics' Chap. VI, Science edit. Wiley, New York, 1960 
  • 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 FUNCTIONAL EQUATIONS IN n-VARIABLES AND ITS APPLICATIONS" Communications of the Korean Mathematical Society = 대한수학회논문집 20 (2): 321~338    
    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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