• 제목/요약/키워드: reciprocal difference functional equation

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STABILITY OF THE RECIPROCAL DIFFERENCE AND ADJOINT FUNCTIONAL EQUATIONS IN THREE VARIABLES

  • Kim, Gwang Hui;Lee, Young Whan
    • Korean Journal of Mathematics
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    • 제18권3호
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    • pp.311-322
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    • 2010
  • In this paper, we prove stabilities of the reciprocal difference functional equation $$r(\frac{x+y+z}{3})-r(x+y+z)=\frac{2r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ and the reciprocal adjoint functional equation $$r(\frac{x+y+z}{3})+r(x+y+z)=\frac{4r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ with three variables. Stabilities of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables was proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar. We extend their results to three variables in similar types.

STABILITY OF THE RECIPROCAL DIFFERENCE AND ADJOINT FUNCTIONAL EQUATIONS IN m-VARIABLES

  • Lee, Young Whan;Kim, Gwang Hui
    • 충청수학회지
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    • 제23권4호
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    • pp.731-739
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    • 2010
  • In this paper, we prove stability of the reciprocal difference functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)-r\(\sum_{i=1}^{m}x_i\)=\frac{(m-1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ and the reciprocal adjoint functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)+r\(\sum_{i=1}^{m}x_i\)=\frac{(m+1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ in m-variables. Stability of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables were proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar [13]. We extend their result to m-variables in similar types.

STABILITY OF THE G-FUNCTIONAL EQUATION

  • Kim, Gwang-Hui
    • Journal of applied mathematics & informatics
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    • 제9권2호
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    • pp.837-844
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    • 2002
  • In this paper, we obtain the Hyers-Ulam Stability for the difference equations of the form f(x + 1) = $\Gamma$(x)f(x), which is the reciprocal functional equation of the double gamma function.