Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function
Huo Tang, G. Murugusundaramoorthy, Shu-Hai Li, Lina Ma
Abstract
<abstract><p>In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\leq \vartheta \leq 1) $\end{document} </tex-math></disp-formula></p> <p>lies in a region starlike with respect to $ 1 $ and symmetric with respect to the real axis. As a special case of this result, the Fekete-Szegö inequality for a class of functions defined through Poisson distribution series is obtained. Further, we discuss the second Hankel inequality for functions in this new class.</p></abstract>