A study of sharp coefficient bounds for a new subfamily of starlike functions

AbstractIn this article, by employing the hyperbolic tangent function tanhz, a subfamily$\mathcal{S}_{\tanh }^{\ast }$Stanh∗of starlike functions in the open unit disk$\mathbb{D}\subset \mathbb{C}$D⊂C:$$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \mathbb{C} \text{ and } \vert z \vert < 1 \bigr\} \end{aligned}$$D={z:z∈C and |z|<1}is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the Taylor–Maclaurin coefficients for functions belonging to the class$\mathcal{S}_{\tanh }^{\ast }$Stanh∗of starlike functions in$\mathbb{D}$D. In particular, the bounds of the first three Taylor–Maclaurin coefficients, the estimates of the Fekete–Szegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here

Third Hankel determinant for starlike and convex functions with respect to symmetric points

The objective of this paper is to obtain best possible upper bound to the $H_{3}(1)$  Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants

Study of Second Hankel Determinant for Certain Subclasses of Functions Defined by Al-Oboudi Differential Operator

هذا البحث يهتم في حساب الحد الأعلى من محدد هانكل الثاني لمجموعة من الدوال المعرفة بالمؤثر التفاضلي للعبودي المعرف على القرص الأحادي. لدراسة الحالات الخاصة من نتائج هذا البحث، اعطى الباحثين قيم خاصة للمؤثرات المعرفة ك A، B وλ.The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and

Sharp bounds of the third Hankel determinant for classes of univalent functions with bounded turning

summary:We improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning