Real fixed points and singular values of two-parameter family lambdafrac{z}{(e^{z}-1)^{n}}

The two-parameter family of f_{lambda,n}(z)=lambda frac{z}{(e^{z}-1)^{n}}, lambda in mathbb{R} backslash {0}, z in mathbb{C} backslash {0}, nin mathbb{N} backslash {1}, is considered in this paper. The existence and nature of the real fixed points of f_{lambda,n}(x), xin {mathbb{R}}setminus {0} are described for n odd and n even. It is found that the function f_{lambda,n}(z) possesses infinitely many singular values. It has also been shown that some critical values of f_{lambda,n}(z) lie in the closure and other lie into the exterior of the disk centered at origin and having radius lambda.