Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function

Abstract

UDC 517.5

We determine the sharp bound of the second-order Hankel determinant $H_{2,2}(f)$ and the coefficient functional for functions from the class of $q$-starlike functions  $ \mathcal{S}^*(\mathcal{L},q)$ by refining the results obtained in [Srivastava et al., Upper bound of the third Hankel determinant for a subclass of $q$-starlike functions associated with the $q$-exponential function, Bull.  Sci. Math., 167 (2021); https://doi.org/10.1016/j.bulsci.2020.102942].  Moreover, we  obtain sharp estimates for the Fekete–Szegö functional and the coefficient differences for the analyzed class of functions.