General form of some rational recursive sequences

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Abstract

In this note, we study the general form of some rational recursive sequences. By some modification of the methods and ideas, as well as the transformation from the paper [K. S. Berenhaut, J. D. Foley and S. Stević, The global attractivity of the rational difference equation yn=ynk+ynm1+ynkynm, Appl. Math. Lett. 20 (2007), 54–58], we give a new proof for the conjectures posed therein.

Keywords

Rational recursive sequence
Attractivity
Positive solution
Equilibrium
Converge

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Supported partly by NNSF of China (Grant: 10771215, 10771094) and Project of Hunan Provincial Youth Key Teacher.