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 A global behavior of the positive solutions of $x_{n+1}=\dfrac{ \beta x_n +x_{n-2}}{A+Bx_n +x_{n-2}}$ Commun. Korean Math. Soc. 2008 Vol. 23, No. 1, 61-65 Printed March 1, 2008 JongAn Park Department of Mathematics, Kangwon National University, Chuncheon 200-701, Korea Abstract : In this paper we prove that every positive solution of the third order rational difference equation $$x_{n+1}=\dfrac{ \beta x_n +x_{n-2}}{A+Bx_n +x_{n-2}}$$ converges to the positive equilibrium point $$\overline{x}=\dfrac{\beta+1-A}{B+1},$$ where \$ 0 Keywords : difference equations, equilibrium point MSC numbers : Primary 39A11 Downloads: Full-text PDF