On the Recursive Sequence ð ‘¥ ð ‘› + ð Ÿ = m a x { ð ‘¥ ð ‘›, ð ´ } / ð ‘¥ ð Ÿ ð ‘› ð ‘¥ ð ‘› − ð Ÿ

Ibrahim Yalcinkaya, Cengiz Cinar and Ali Gelisken

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-13

Abstract:

We investigate the periodic nature of the solution of the max-type difference equation ð ‘¥ ð ‘› + 1 = m a x { ð ‘¥ ð ‘› , ð ´ } / ð ‘¥ 2 ð ‘› ð ‘¥ ð ‘› − 1 , ð ‘› = 0 , 1 , 2 , … , where the initial conditions are ð ‘¥ − 1 = ð ´ ð ‘Ÿ 1 and ð ‘¥ 0 = ð ´ ð ‘Ÿ 2 for ð ´ âˆˆ ( 0 , ∞ ) , and that ð ‘Ÿ 1 and ð ‘Ÿ 2 are positive rational numbers. The results in this paper solve the Open Problem proposed by Grove and Ladas (2005).

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:583230

DOI: 10.1155/2010/583230

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