Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지

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

  • Kim, Gwang Hui (Department of Mathematics Kangnam University) ;
  • Lee, Young Whan (Department of Computer Hacking and Information Security College of Natural Science Daejeon University)
  • Received : 2010.08.21
  • Accepted : 2010.09.10
  • Published : 2010.09.30
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Abstract

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.

Keywords

References

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