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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)
Publication Information
Korean Journal of Mathematics / v.18, no.3, 2010 , pp. 311-322 More about this Journal
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
reciprocal difference functional equation; reciprocal adjoint functional equation; generalized Hyers-Ulam Stability;
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