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Focus in this paper is on the Hankel determinant, $H_3(1)$, for the well-known classes of bounded-turning, starlike and convex functions in the open unit disk $E=\{z\in \mathbb{C}\colon|z|<1\}$. The results obtained complete the series of…
Recently, the subclass of starlike functions associated with exponential function $e^z$, given by ${S}^*_e = \{f(z)\in {S}:{zf'(z)}/{f(z)} \prec e^z, (z\in \mathbb{D}) \}$ was introduced and studied by Mendiratta $et$ $al.$…
In the present study, we consider two subclasses starlike and convex functions, denoted by $\mathcal{S}_{\mathcal{B}}^{*}$ and $\mathcal{C}_{\mathcal{B}}$ respectively, associated with a bean-shaped domain. Further, we estimate certain…
In this paper we give the upper bounds of the Hankel determinants of the second and third order for the class $\mathcal{S}$ of univalent functions in the unit disc.
The sharp bound for the third Hankel determinant for the coefficients of the inverse function of starlike function of order $1/2$ is obtained. In light of this, we can deduce that the functionals $|H_3(1)(f)|$ and $|H_3(1)(f^{-1})|$ exhibit…
In this paper we improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning. The bounds are not sharp, but the sharp ones are conjectured.
In this paper we give improved, probably not sharp, upper bounds of the Hankel determinant of third order for various classes of univalent functions and conjecture the sharp one.
In this paper, we obtain sharp bounds for the third Hankel determinants of the coefficients of the inverse of bounded turning functions. Thus answering a negatively to a conjecture recently posed regarding these functions. Additionally, we…
This paper deals with sharp bounds for the third-order Hankel, Toeplitz and Hermitian-Toeplitz determinant of functions belonging to the class $\mathcal{S}^*_{B}$ of starlike functions associated with a balloon-shaped domain, given by \[…
The aim of the present paper is to obtain the sharp bounds of the Hankel determinants H_2(3) and H_3(1) for the well known class SL^* of starlike functions associated with the right lemniscate of Bernoulli. Further for n=3, we find the…
Using some properties of the Grunsky coefficients we improve earlier results for upper bounds of the Hankel determinants of the second and third order for the class $\mathcal{S}$ of univalent functions.
In this paper we determine the upper bounds of $|H_{2}(3)|$ for the inverse functions of functions of some classes of univalent functions, where $H_{2}(3)(f)=a_{3}a_{5}-a_{4}^{2}$ is the Hankel determinant of a special type.
In this paper we determine the upper bounds of the Hankel determinants of special type $H_{2}(3)(f)$ and $H_{2}(4)(f)$ for the class of univalent functions and for the class $\mathcal{U}$ defined by \[ \mathcal{U}=\left\{ f\in\mathcal{A} :…
We prove a conjecture concerning the third Hankel determinant, proposed in ``Anal. Math. Phys., https://doi.org/10.1007/s13324-021-00483-7", which states that $|H_3(1)|\leq 1/9$ is sharp for the class $\mathcal{S}_{\wp}^{*}=\{zf'(z)/f(z)…
For $f\in \mathcal{S}$, the class univalent functions in the unit disk $\mathbb{D}$ and given by $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ for $z\in \mathbb{D}$, we improve previous bounds for the second and third Hankel determinants in case…
Let $\mathcal{A}$ denote the class of analytic functions such that $f(0)=0$ and $f'(0)=1$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}.$ In this paper, we consider $\mathcal{S}^*(\varphi) := \left\{ f \in \mathcal{A} :…
In the present investigation, we consider a subclass of starlike functions associated with a petal shaped domain, recently introduced and defined by $$\mathcal{S}^{*}_{\rho}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\sinh^{-1} z\}.$$ We…
Logarithmic coefficients play a crucial role in the theory of univalent functions. In this study,we focus on the classes $\mathcal{S}_e^\ast$ and $\mathcal{C}_e$ of starlike and convex functions, respectively, \begin{align*}…
Following the trend of coefficient bound problems in Geometric Function Theory, in the present paper, we obtain the sharp bound of $|H_3(1)|$ for the class $\mathcal{S}^*$, of starlike functions and $\mathcal{SL}_q^*$, of $q$- starlike…
In this paper, sharp bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.