Univalence criteria and analogs of the John constant

Yong Chan Kim, Toshiyuki Sugawa

Let $p(z)=z{f}^{\prime }(z)/f(z)$ for a function $f(z)$ analytic on the unit disk $|z|<1$ in the complex plane and normalized by $f(0)=0,f^{\prime }(0)=1.$ We will provide lower and upper bounds for…