Geodesic
Singular values and fixed points of family of generating function of Bernoullis numbers
Sajid, Mohammad1
1 College of Engineering, Qassim University, Buraidah, Al-Qassim, Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 1, p. 17-22.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Singular values and fixed points of one parameter family of generating function of Bernoulli's numbers, $g_\lambda(z) = \lambda\frac{z}{e^z-1} , \lambda\in \mathbb{R}-\{0\}$, are investigated. It is shown that the function $g_\lambda(z)$ has infinitely many singular values and its critical values lie outside the open disk centered at origin and having radius $\lambda$. Further, the real fixed points of $g_\lambda(z)$ and their nature are determined. The results found are compared with the functions $\lambda\tan z, E_\lambda(z) = \lambda \frac{e^z-1}{z}$ and$ f_\lambda(z) = \lambda \frac{z}{z+4}e^z$ for $\lambda > 0$.
DOI : 10.22436/jnsa.008.01.03
Classification : 30D05, 37C25, 58K05
Keywords: Fixed points, critical values, singular values.

Sajid, Mohammad 1

1 College of Engineering, Qassim University, Buraidah, Al-Qassim, Saudi Arabia 
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Sajid, Mohammad. Singular values and fixed points of family of generating function of Bernoullis numbers. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 1, p. 17-22. doi : 10.22436/jnsa.008.01.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.01.03/

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