Nonlinear extremal problems for analytic two-dimensional Riemann- Stieltjes integrals (Q1122025)

Let D denote the unit disc. The author considers functions \[ \phi (z)=\int_{D}z d\mu (\zeta)/1-z\zeta,\quad z\in D, \] where \(\mu\) is a unit mass measure on D resp. functions \(f(z)=\phi (1/z)\). For the class of such functions he determines the maximal domain of univalence and the radii of starlikeness and convexity of order \(\alpha\), \(-\infty <\alpha <1\).