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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 (difference equations) 39A20 Generalized difference equations
Full Text:
References:
 [1] Berenhaut, K.; Foley, J.; Stević, S.: Boundedness character of positive solutions of a MAX difference equation, J. differ. Equat. appl. 12, No. 12, 1193-1199 (2006) · Zbl 1116.39001 · doi:10.1080/10236190600949766 [2] ç, C.; Inar; Stević, S.; Yalçinkaya, I.: On positive solutions of a reciprocal difference equation with minimum, J. appl. Math. comput. 17, No. 1 -- 2, 307-314 (2005) [3] Elsayed, E. M.; Stević, S.: On the MAX-type equation xn+1=maxAxn,xn-2, 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, No. 4, 77-85 (2000) · Zbl 1039.39005 [5] S. Stević, Some open problems and conjectures on difference equations, %3chttp://www.mi.sanu.ac.yu/colloquiums/mathcoll_programs/mathcoll.apr2004.htm%3e. [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 xn+1=A+xnp/xn-1r, Discrete dyn. Nat. soc. 2007, 9 (2007) · Zbl 1151.39011 · doi:10.1155/2007/40963 [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 $xn+1=max{c,xnp/xn-1p}$, Appl. math. Lett. 21, No. 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 · doi:10.1016/j.na.2008.01.014 [11] Stević, S.: Global stability of a difference equation with maximum, Appl. math. Comput. 210, 525-529 (2009) · Zbl 1167.39007 · doi:10.1016/j.amc.2009.01.050 [12] Sun, F.: On the asymptotic behavior of a difference equation with maximum, Discrete dyn. Nat. soc. 2008, 6 (2008) · Zbl 1155.39008 · doi:10.1155/2008/243291 [13] Yalçinkaya, I.; Iričanin, B. D.; ç, C.; Inar: On a MAX-type difference equation, Discrete dyn. Nat. soc. 2007, 11 (2007) [14] Yang, X.; Liao, X.: On a difference equation with maximum, Appl. math. Comput. 181, 1-5 (2006) · Zbl 1148.39303 · doi:10.1016/j.amc.2006.01.005