On real fixed points of one parameter family of Function x/${(b^{x}-1)}$

Mohammad Sajid


In the present paper, the real fixed points of one parameter family ${\cal T}=\{f_{\lambda}(x)$$=\lambda\frac{x}{b^{x}-1}\; \text{and}\;f_{\lambda}(0)=\frac{\lambda}{\ln b} : \lambda>0, x \in \mathbb{R},b>0, b\neq 1\}$ are investigated. Further, the nature of these fixed points of $f_{\lambda}(x)$ are shown for $b>0$ except $b=1$.


Fixed points

Full Text:



Alan F. Beardon, Iteration of Rational Functions, Springer, New York, 2000.

R. L. Devaney, $e^{z}$ - {D}ynamics and Bifurcation, International Journal of Bifurcations and Chaos, 1(1991), 287--308.

X. H. Hua and C. C. Yang, Dynamics of Transcendental Functions, Gordan and Breach Sci. Pub.,Amsterdam, 1998.

G. P. Kapoor and M. Guru Prem Prasad, Dynamics of $(e^{z} -1)/z$: the Julia set and Bifurcation, Ergodic Theory and Dynamical Systems, 18(6)(1998), 1363--1383.

Tarakanta Nayak and M. Guru Prem Prasad, Iteration of certain meromorphic functions with unbounded singular values}, Ergodic Theory and Dynamical Systems, 30(3) (Jun 2010), 877--891.

M. Guru Prem Prasad, Chaotic burst in the dynamics of

$f_{lambda}(z)=lambda frac{sinh(z)}{z}$, Regular and Chaotic Dynamics, 10(1) (2005), 71--80.

M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of

certain class of critically bounded entire transcendental functions, J. Math. Anal. Appl., 329(2)(2007), 1446--1459.

M. Sajid and G. P. Kapoor, Dynamics of a family of non-critically finite even transcendental meromorphic functions, Regular and Chaotic Dynamics,9(2) (2004), 143--162.

DOI: http://dx.doi.org/10.5556/j.tkjm.46.2015.1577

Sponsored by Tamkang University | ISSN 0049-2930 (Print), ISSN 2073-9826 (Online) | Powered by MathJax