A Global Convergence Result for a Higher Order Difference Equation

Bratislav D. Iricanin

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-7

Abstract:

Let f ( z 1 , … , z k ) ∈ C ( I k , I ) be a given function, where I is (bounded or unbounded) subinterval of ℠, and k ∈ ℕ . Assume that f ( y 1 , y 2 , … , y k ) ≥ f ( y 2 , … , y k , y 1 ) if y 1 ≥ max { y 2 , … , y k } , f ( y 1 , y 2 , … , y k ) ≤ f ( y 2 , … , y k , y 1 ) if y 1 ≤ min { y 2 , … , y k } , and f is non- decreasing in the last variable z k . We then prove that every bounded solution of an autonomous difference equation of order k , namely, x n = f ( x n − 1 , … , x n − k ) , n = 0 , 1 , 2 , … , with initial values x − k , … , x − 1 ∈ I , is convergent, and every unbounded solution tends either to + ∞ or to − ∞ .

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2007/091292.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2007/091292.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:091292

DOI: 10.1155/2007/91292

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().