On the radius of convexity of order \(\alpha\) of the totally monotonic functions (Q749699)

Let \(\mu\) be a probability measure on [0,1] and T the class of analytic functions f of the form \(f(z)=\int^{1}_{0}\frac{zd\mu (t)}{1-zt}\). The author determines \(\min \{Re(1+\frac{zf''(z)}{f'(z)})| f\in T\}\) for any \(z,| z| <1\).