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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:
39A30Stability theory (difference equations)
39A20Generalized difference equations
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]&ccedil, 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)
[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,
[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=maxc,xnp/xn-1p, Appl. math. Lett. 21, No. 8, 791-796 (2008)
[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.; &ccedil, 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