Singular Values of One Parameter Family \(λ ((e^z-1)/z)^m\) - Sajid, Mohammad (International Journal of Applied Mathematical Research, 2015)
In the present paper, the singular values of one parameter family of entire functions \(f_λ(z)=λ(e^z-1z)^m\) and \(f_λ(0)=λ\), \(mN{0}\), \(λR {0}\), \(z C\) is investigated. It is shown that all the critical values of \(f_λ(z)\) lie in the left half plane. It is also found that the function \(f_λ(z)\) has infinitely many bounded singular values and lie inside the open disk centered at origin and having radius \(|λ|\).