Inclusion relations and radius problems for a subclass of starlike functions
J. Korean Math. Soc. 2021 Vol. 58, No. 5, 1147-1180
Published online June 2, 2021
Printed September 1, 2021
Prachi Gupta, Sumit Nagpal, Vaithiyanathan Ravichandran
University of Delhi; University of Delhi; National Institute of Technology
Abstract : By considering the polynomial function $\phi_{car}(z)=1+z+z^2/2,$ we define the class $\Scar$ consisting of normalized analytic functions $f$ such that $zf'/f$ is subordinate to $\phi_{car}$ 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.
Keywords : Subordination, close-to-convex, starlike, cardioid, inclusion relation, radius problem, partial sum, convolution
MSC numbers : 30C45, 30C80
Supported by : The first author is supported by a Junior Research Fellowship from Council of Scientific and Industrial Research (CSIR), New Delhi with File No. 09/045(1727)/2019-EMR-I.
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