Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(5): 1147-1180

Online first article June 2, 2021      Printed September 1, 2021

https://doi.org/10.4134/JKMS.j200465

Copyright © The Korean Mathematical Society.

Inclusion relations and radius problems for a subclass of starlike functions

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.