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 Inclusion Relations and Radius Problems for a subclass of starlike functions J. Korean Math. Soc.Published online June 2, 2021 Prachi Gupta, Sumit Nagpal, and V. Ravichandran Department of Mathematics, University of Delhi, Ramanujan College, University of Delhi, National Institute of Technology, Tiruchirappalli Abstract : By considering the polynomial function $\phi_{car}(z)=1+z+z^2/2,$ we define the class $\mathcal{S}^*_{car}$ 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 $\mathcal{S}^*_{car}$ 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 Full-Text :