Related papers: The sharp bound of the third Hankel determinant fo…

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…

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 improve the upper bound of the third order Hankel determinant for the class of Ozaki close-to-convex functions. The sharp bound is conjectured.

The aim of this paper is to obtain an upper bound to the second Hankel the determinant for starlike and convex functions of order.

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.

Let $f$ be analytic in the unit disk $\mathbb{D}= \{z \in \mathbb{C}~:~ |z| < 1\}$, and $\mathcal{S}$ be the subclass of normalized univalent functions given by $f(z)=\sum_{n=1}^{\infty}a_{n}z^{n},~a_{1}:=1$ for $z \in\mathbb{D}$. We…

Let ${\mathcal A}$ be the class of functions that are analytic in the unit disc ${\mathbb D}$, normalized such that $f(z)=z+\sum_{n=2}^\infty a_nz^n$, and let class ${\mathcal U}(\lambda)$, $0<\lambda\le1$, consists of functions…

In this paper, we obtain the upper bounds to the third Hankel determinants for starlike functions of order $\alpha$, convex functions of order $\alpha$ and bounded turning functions of order $\alpha$. Furthermore, several relevant results…

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 provide an estimation for the sharp bound of the third Hankel determinant of starlike functions of order $\alpha$, where $\alpha$ ranges in the interval $[0, 1/6]\cup \{1/2\}$ and thereby extending the result of Rath et…

In this paper, we obtain the sharp bounds of the second Hankel determinant of logarithmic inverse coefficients for the starlike and convex functions.

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 obtain the sharp bounds of the second Hankel determinant of logarithmic inverse coefficients for the strongly starlike and strongly convex functions of order alpha.

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…

Let $f$ be analytic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order $\alpha$,…

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.

In this paper, we consider the class of strongly bi-close-to-convex functions of order $\alpha$ and bi-close-to-convex functions of order $\beta$. We obtain an upper bound estimate for the second Hankel determinant for functions belonging…

In the present investigation the authors obtain upper bounds for the second Hankel determinant of the classes bi-starlike and bi-convex functions of order beta.

In this note, we present the determinant, the inverse and a lower bound for the smallest eigenvalue for some Hankel matrices

In this paper, sharp bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.