Singular values and fixed points of family of generating function of Bernoulli s numbers

Singular values and fixed points of one parameter family of generating function of Bernoulli s numbers, \(g_λ(z) = λ\frac{z}{e^z1} , λ\in \mathbb{R}\{0\}\), are investigated. It is shown that the function \(g_λ(z)\) has infinitely many singular values and its critical values lie outside the open disk centered at origin and having radius \(\λ\). Further, the real fixed points of \(g_λ(z)\) and their nature are determined. The results found are compared with the functions λ\tan z, E λ(z) = λ \frac{e^z1}{z}\) and\( f λ(z) = λ \frac{z}{z+4}e^z\) for λ 0.