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Real Dynamics of Family of Functions λxe<sup>x</sup>/(e<sup>x</sup>-1) for Positive λ
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Real Dynamics of Family of Functions λxex/(ex-1) for Positive λ

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Abstract:

In this paper, the real dynamics of one parameter family of functions hλ(x)=λxex(ex-1), λ>0 is investigated. It is shown that the real fixed point of hλ(x) exists only for 0<λ<1 which is attracting and there is no real fixed point for λ>1 It is found that the whole real line converges to real attracting fixed point of hλ(x) for 0<λ<1.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 8)
Pages:
60-61
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.8.60
Citation:
M. Sajid, "Real Dynamics of Family of Functions λxex/(ex-1) for Positive λ", Bulletin of Mathematical Sciences and Applications, Vol. 8, pp. 60-61, 2014
Online since:
May 2014
Authors:
Mohammad Sajid
Keywords:
Fixed Points
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Distribution:
Open Access

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This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

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S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge University Press, Cambridge (2000).

Tarakanta Nayak and M. Guru Prem Prasad, Iteration of certain Meromorphic Functions with Unbounded Singular Values, Ergodic Theory and Dynamical Systems, 30, No 3 (Jun 2010), 877- 891.

M. Sajidand G. P. Kapoor, Dynamics of Transcendental Meromorphic Functions ( z   )e z /(z    4) : having rational Schwarzian Derivative, Dynamical systems: An International Journal, 22, No 3 (2007), 323-337.

M. Sajid, Singular Values and Fixed Points of Family of Function Math., 27, No 2 (2014), 147-154. ( ze z ) /(e z  1), Int. J. Appl.

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