Starlike functions associated with $ \tanh z $ and Bernardi integral operator

Abstract

<p style='text-indent:20px;'>We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function <inline-formula><tex-math id="M8">\begin{document}$ \tanh z $\end{document}</tex-math></inline-formula>. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.</p>