Weak quasicircles have Lipschitz dimension 1

We prove that the Lipschitz dimension of any bounded turning Jordan circle or arc is equal to 1. Equivalently, the Lipschitz dimension of any weak quasicircle or arc is equal to 1.

The sharp bound of the third Hankel determinant for functions of bounded turning

We find the sharp bound for the third Hankel determinant $$\begin{aligned} H_{3,1}(f):= \left| {\begin{array}{*{20}c} {a_{1} } & {a_{2} } & {a_{3} } \\ {a_{2} } & {a_{3} } & {a_{4} } \\ {a_{3} } & {a_{4} } & {a_{5} } \\ \end{array} } \right| \end{aligned}$$ H 3 , 1 ( f ) : = a 1 a 2 a 3 a 2 a 3 a 4 a 3 a 4 a 5 for analytic functions f with $$a_n:=f^{(n)}(0)/n!,\ n\in \mathbb N,\ a_1:=1,$$ a n : = f ( n ) ( 0 ) / n ! , n ∈ N , a 1 : = 1 , such that $$\begin{aligned} {{\,\mathrm{Re}\,}}f'(z)>0,\quad z\in \mathbb D:=\{z \in \mathbb C: |z|<1\}. \end{aligned}$$ Re f ′ ( z ) > 0 , z ∈ D : = { z ∈ C : | z | < 1 } .

A Study of Third and Fourth Hankel Determinant Problem for a Particular Class of Bounded Turning Functions

In this present paper, a new generalized class ℛ p , q from the family of function with bounded turning was introduced by using p , q - derivative operator. Our aim for this class is to find out the upper bound of third- and fourth-order Hankel determinant. Moreover, the upper bounds for two-fold and three-fold symmetric functions for this class are also obtained.

Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain

In this research article we consider two well known subclasses of starlike and bounded turning functions associated with nephroid domain. Our aims to find third Hankel determinant for these classes.

Sharp Bounds of the Coefficient Results for the Family of Bounded Turning Functions Associated with a Petal-Shaped Domain

The goal of this article is to determine sharp inequalities of certain coefficient-related problems for the functions of bounded turning class subordinated with a petal-shaped domain. These problems include the bounds of first three coefficients, the estimate of Fekete-Szegö inequality, and the bounds of second- and third-order Hankel determinants.

Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function

The Hankel determinant for a function having power series was first defined by Pommerenke. The growth of Hankel determinant has been evaluated for different subcollections of univalent functions. Many subclasses with bounded turning are several interesting geometric properties. In this paper, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order. Our purpose is to obtain some upper bounds for the third and fourth Hankel determinants related to such classes.

Coefficient functionals for a class of bounded turning functions related to modified sigmoid function

<abstract><p>The main objective of the present article is to define the class of bounded turning functions associated with modified sigmoid function. Also we investigate and determine sharp results for the estimates of four initial coefficients, Fekete-Szegö functional, the second-order Hankel determinant, Zalcman conjucture and Krushkal inequality. Furthermore, we evaluate bounds of the third and fourth-order Hankel determinants for the class and for the 2-fold and 3-fold symmetric functions.</p></abstract>