Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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STABILITY OF THE RECIPROCAL DIFFERENCE AND ADJOINT FUNCTIONAL EQUATIONS IN m-VARIABLES

  • Lee, Young Whan (Department of Computer Hacking and Information Security Daejeon University) ;
  • Kim, Gwang Hui (Department of Mathematics Kangnam University)
  • Received : 2010.08.24
  • Accepted : 2010.11.09
  • Published : 2010.12.30
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Abstract

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.

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References

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