Coefficient Functionals for Starlike Functions of Reciprocal Order

Abstract

Several properties of the class $\mathcal{S}^*_{r}(\alpha)$ of starlike functions of reciprocal order $\alpha\,(0\leq \alpha <1)$ defined on the open unit disk have been studied in this paper. The paper begins with a sufficient condition for analytic functions to be in the class $\mathcal{S}^*_{r}(\alpha)$. Further, the sharp bounds on third order Hermitian-Toeplitz determinant, initial inverse coefficients and initial logarithmic coefficients for functions in the class $\mathcal{S}^*_{r}(\alpha)$ are derived.