Sharp coefficient bounds for starlike functions associated with the Bell numbers

By Virendra Kumar, Nak Eun Cho, V. Ravichandran, H. M. Srivastava. Mathematica Slovaca, 2019

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Abstract Let SB∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ be the class of normalized starlike functions associated with a function related to the Bell numbers. By establishing bounds on some coefficient functionals for the family of functions with positive real part, we derive for functions in the class SB∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants. Bounds on the first three consecutive higher-order Schwarzian derivatives for functions in the class SB∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ are investigated.

Subfields: Applied Mathematics, Electronic, Optical and Magnetic Materials, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f958576ede1645a65325a8e92b16169480ca9dcb