Geometric properties of solutions of a class of differential equations
The paper is concerned with a few geometric properties of the solutions of the second order linear differential equations \[ w''(z) + a(z) w'(z) + b(z) w(z) = 0, \] with coefficients analytic in the open unit disk. Under several boundedness assumptions on the coefficients, the authors obtain estimations of \(\Re \frac{zw'(z)}{w(z)}\) or \(\frac{zw'(z)}{w(z)}\). These results then imply, in different situations, the solutions to be starlike. The proof is based on an earlier result due to \textit{H. Saitoh} [Ann. Univ. Mariae Curie-Sklodowska, Sect. A 53, 209--216 (1999; Zbl 0984.30007)].
scientific article; zbMATH DE number 2142419