Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk). (10th May 2015)

• Record Type: Journal Article
• Authors: Bakery, Awad A.
• Other Names: Chung Jaeyoung Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-05-10
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/737420
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We give in this work the sufficient conditions on the positive solutions of the difference equationx n + 1 = α + ( x n - 1 m / x n k ), n = 0, 1, …, where α, k, andm ∈ ( 0, ∞ ) under positive initial conditionsx - 1, x 0 to be bounded, α -convergent, the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime two-periodic solution. Our results coincide with that known for the casesm = k = 1 of Amleh et al. (1999) andm = 1 of Hamza and Morsy (2009). We offer improving conditions in the case ofm = 1 of Gümüs and Öcalan (2012) and explain our results by some numerical examples with figures.