Singular Values of One Parameter Family \(\lambda ((e^{z}-1)/z)^{m}\)

In the present paper, the singular values of one parameter family of entire functions $f_{\lambda}(z)=\lambda\bigg(\dfrac{e^{z}-1}{z}\bigg)^{m}$ and $f_{\lambda}(0)=\lambda$, $m\in \mathbb{N}\backslash \{0\}$, $\lambda\in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C}$ is investigated. It is shown that all the critical values of $f_{\lambda}(z)$ lie in the left half plane. It is also found that the function $f_{\lambda}(z)$ has infinitely many bounded singular values and lie inside the open disk centered at origin and having radius $|\lambda|$.