On the Recursive Sequence xn+1=max {xn, A}/xn2xn−1. (8th June 2010)

• Record Type: Journal Article
• Authors: Yalcinkaya, Ibrahim; Cinar, Cengiz; Gelisken, Ali
• Other Names: Zhang Guang Y. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2010(2010)
• Publication Date: 2010-06-08
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2010/583230
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We investigate the periodic nature of the solution of the max-type difference equationx n + 1 = max { x n, A } / x n 2 x n - 1, n = 0, 1, 2, …, where the initial conditions arex - 1 = A r 1 andx 0 = A r 2 forA ∈ ( 0, ∞ ), and thatr 1 andr 2 are positive rational numbers. The results in this paper solve the Open Problem proposed by Grove and Ladas (2005).