TY - JOUR
AU - Masih, Vali Soltani
AU - Ebadian, Ali
AU - Sokol, Janusz
PY - 2022/08/01
Y2 - 2022/10/06
TI - On Strongly Starlike Functions Related to the Bernoulli Lemniscate
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 53
IS - 3
SE - Papers
DO - 10.5556/j.tkjm.53.2022.3234
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3234
SP - 187-199
AB - <p>Let $\mathcal{S}^{\ast}_{L}(\lambda)$ be the class of functions $f$, analytic in the unit disc $\Delta=\{z:|z|<1\}$, with the normalization $f(0)=f'(0)-1=0$, which satisfy the condition<br />\begin{equation*}<br />\frac{zf'(z)}{f(z)}\prec \left(1+z\right)^{\lambda},<br />\end{equation*}<br />where $\prec$ is the subordination relation. The class $\mathcal{S}^{\ast}_{L}(\lambda)$ is a subfamily of the known class of strongly starlike functions of order $\lambda$. In this paper,<br />the relations between $\mathcal{S}^{\ast}_{L}(\lambda)$ and other classes geometrically defined are considered. Also, we obtain some characteristics such as, bounds for coefficients, radius of convexity, the Fekete-Szeg\"{o} inequality, logarithmic coefficients and the second Hankel determinant inequality for functions belonging to this class. The univalent functions $f$ which satisfy the condition<br />\begin{equation*}<br />\Re\left\{1+\frac{zf''(z)}{f'(z)}\right\}<1+\frac{\lambda}{2},\qquad<br />(z \in \Delta)\end{equation*}<br />are also considered here.</p>
ER -