On power deformations of univalent functions

Yong Chan Kim, Toshiyuki Sugawa

For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f^{\prime }(0)-1=0$ and $f(z)\ne 0,0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z{)}^c$ for a complex number…