## Global stability of a max-type difference equation.(English)Zbl 1193.39009

A global stability result is proved for a difference equation of max-type. The result improves the main theorem from a recent paper of the author.

### MSC:

 39A30 Stability theory for difference equations 39A20 Multiplicative and other generalized difference equations
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### References:

 [1] Berenhaut, K.; Foley, J.; Stević, S., Boundedness character of positive solutions of a MAX difference equation, J. differ. equat. appl., 12, 12, 1193-1199, (2006) · Zbl 1116.39001 [2] Çinar, C.; Stević, S.; Yalçinkaya, I., On positive solutions of a reciprocal difference equation with minimum, J. appl. math. comput., 17, 1-2, 307-314, (2005) · Zbl 1074.39002 [3] Elsayed, E.M.; Stević, S., On the MAX-type equation $$x_{n + 1} = \max \left\{\frac{A}{x_n}, x_{n - 2}\right\}$$, Nonlinear anal. TMA, 71, 910-922, (2009) · Zbl 1169.39003 [4] Stević, S., Behavior of the positive solutions of the generalized beddington – holt equation, Panamer. math. J., 10, 4, 77-85, (2000) · Zbl 1039.39005 [5] S. Stević, Some open problems and conjectures on difference equations, [6] S. Stević, Boundedness character of a max-type difference equation, in: Conference in Honour of Allan Peterson, Book of Abstracts, Novacella, Italy, July 26-August 02, 2007, p. 28. [7] Stević, S., On the recursive sequence $$x_{n + 1} = A + x_n^p / x_{n - 1}^r$$, Discrete dyn. nat. soc., 2007, 9, (2007), Article ID 40963 · Zbl 1151.39011 [8] S. Stević, On behavior of a class of difference equations with maximum, Mathematical Models in Engineering, Biology and Medicine. Conference on Boundary Value Problems. Book of Abstracts, Santiago de Compostela, Spain, September 16-19, 2008, p. 35. [9] Stević, S., On the recursive sequence $$x_{n + 1} = \max \{c, x_n^p / x_{n - 1}^p \}$$, Appl. math. lett., 21, 8, 791-796, (2008) · Zbl 1152.39012 [10] Stević, S., Boundedness character of a class of difference equations, Nonlinear anal. TMA, 70, 839-848, (2009) · Zbl 1162.39011 [11] Stević, S., Global stability of a difference equation with maximum, Appl. math. comput., 210, 525-529, (2009) · Zbl 1167.39007 [12] Sun, F., On the asymptotic behavior of a difference equation with maximum, Discrete dyn. nat. soc., 2008, 6, (2008), Article ID 243291 · Zbl 1155.39008 [13] Yalçinkaya, I.; Iričanin, B.D.; Çinar, C., On a MAX-type difference equation, Discrete dyn. nat. soc., 2007, 11, (2007), Article ID 47264 · Zbl 1152.39016 [14] Yang, X.; Liao, X., On a difference equation with maximum, Appl. math. comput., 181, 1-5, (2006) · Zbl 1148.39303
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