Inclusion relations and radius problems for a subclass of starlike functions

Abstract

By considering the polynomial function ${\varphi }_{car}(z)=1+z+z^2/2,$ we define the class $\Scar$ consisting of normalized analytic functions $f$ such that $z{f}^{\prime }/f$ is subordinate to ${\varphi }_{car}$ in the unit disk. The inclusion relations and various radii constants associated with the class $\Scar$ and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

References in corpus (3)

• On the radius constants for classes of analytic functions
• Geometric Properties of Partial Sums of Univalent Functions
• Starlikeness of certain analytic functions