We use $\ z^{-1} \xrightarrow{} \frac{z^{-1}-\alpha}{1-{\alpha}z^{-1}}$ and $ \alpha = \frac{\sin(\omega_c^{'}-\omega_c)/2}{\sin(\omega_c^{'}+\omega_c)/2}$ for a lowpass-to-lowpass frequency transformation, where $\omega'_c$ is the cut-off frequency of the prototype lowpass filter, and $\omega_c$ is the cut-off frequency of the transformed lowpass filter.
In practice we know the desired edge frequencies $\ \omega_s$ and $\ \omega_p$ and we are required to find the prototype lowpass cutoff frequencies $\ \omega_s^{'}$ and $\ \omega_p^{'}$.
For calculating $\ \alpha$ we have to know $\ \omega_c^{'}$ . If we calculate $\ \alpha$ we can have $\ \omega_s^{'}$ by $\ \omega_s^{'} = \angle{(\frac{e^{-j\omega_s}+\ \alpha}{1-\alpha e^{-j\omega_s}})}$ But I don't know how select a suitable $\ \omega_p^{'}$.