• 제목/요약/키워드: (modified)Hyers-Ulam-Rassias stability

검색결과 8건 처리시간 0.019초

On a general hyers-ulam stability of gamma functional equation

  • Jung, Soon-Mo
    • 대한수학회보
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    • 제34권3호
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    • pp.437-446
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    • 1997
  • In this paper, the Hyers-Ulam stability and the general Hyers-Ulam stability (more precisely, modified Hyers-Ulam-Rassias stability) of the gamma functional equation (3) in the following setings $$ \left$\mid$ f(x + 1) - xf(x) \right$\mid$ \leq \delta and \left$\mid$ \frac{xf(x)}{f(x + 1)} - 1 \right$\mid$ \leq \frac{x^{1+\varepsilon}{\delta} $$ shall be proved.

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LOCAL STABILITY OF CAUCHY FUNCTIONAL EQUATION

  • Park, Kyoo-Hong;Lee, Young-Whan;Ji, Kyoung-Sihn
    • Journal of applied mathematics & informatics
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    • 제8권2호
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    • pp.581-590
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    • 2001
  • In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.

THE STABILITY OF THE GENERALIZED FORM FOR THE GAMMA FUNCTIONAL EQUATION

  • Kim, Gwang-Hui;Lee, Young-Whan
    • 대한수학회논문집
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    • 제15권1호
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    • pp.45-50
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    • 2000
  • The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.

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ON THE HYERS-ULAM-RASSIAS STABILITY OF A MODIFIED ADDITIVE AND QUADRATIC FUNCTIONAL EQUATION

  • Jun, Kil-Woung;Kim, Hark-Mann;Lee, Don-O
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제11권4호
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    • pp.323-335
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    • 2004
  • In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

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THE STABILITY OF A MIXED TYPE FUNCTIONAL INEQUALITY WITH THE FIXED POINT ALTERNATIVE

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • 대한수학회논문집
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    • 제19권2호
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    • pp.253-266
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    • 2004
  • In this note, by using the fixed point alternative, we investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional inequality which is either cubic or quadratic: $\parallel$8f(x-3y) + 24f(x+y) + f(8y) -8〔f(x+3y) + 3f(x-y) + 2f(2y)〕$\parallel$$\leq$$\varphi$(x,y).