GLOBAL ATTRACTIVITY IN A FOUR-TERM RECURRENCE RELATION

Authors

  • LONG-TU LI Department of Mathematics, Wuyi Univeristy, Jiangmen, Gauagdong, 529020, P. R. China.
  • SUI SUN CHENG Department of Mathematics, Tshing Hua University, Hsinchu, Taiwan 30043, R. O. C.

DOI:

https://doi.org/10.5556/j.tkjm.30.1999.4229

Keywords:

Equilibrium point, four-term recurrence relation, attractivity, difference equation

Abstract

Positive solutions of the four-term recurrence relation $x_{n+1}=f(x_n)g(x_{n-1}, x_{n-2})$ are shown to converge to its positive equalibrium points under relative mild conditions.

References

V. L. Kocic and G. Ladas, Global asymptotic behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht, 1993.

E. Camouzis, E. A. Grove, G. Ladas and V. L. Kocic, Monotone unstable solutions of difference equations and conditons for boundedness, J. Difference Eq. Appl. 1(1995), 17- 44.

L. T. Li, Q. S. Qiu and Z. Yu, Permanence of $x_{n+1} = x_n^2 f(x_n)g(x_{n-1})$, J. Difference Eq Appl. 2(1996), 333-338.

L T. Li, Global asymptotic stability of $x_{n+1} =F(x_n)g(x_{n-1})$, Ann. Diff. Eq., to appear.

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Published

2021-05-01

How to Cite

LI, L.-T., & CHENG, S. S. (2021). GLOBAL ATTRACTIVITY IN A FOUR-TERM RECURRENCE RELATION. Tamkang Journal of Mathematics, 30(3), 223–229. https://doi.org/10.5556/j.tkjm.30.1999.4229

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