Sharp initial coefficient bounds of starlike functions associated with Pascal snail function

Abstract

For $-1 \leq \beta \leq 1$, $ST[\beta]$ is the subclass of generalized Pascal snail function defined by $zf^\prime(z)/f(z) \prec 1 /(1-\beta z)$. In this article, we have presented the coefficient bounds for the analytic functions lying in the class $ST[\beta]$. We have also presented the bounds for the Hankel determinants $|H_{2,1}(f)|$ and $|H_{2,2}(f)|$. The bounds presented in this paper are sharp and the extremal function for each bound is also given.