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

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Gaganpreet Kaur ◽  
Gurmeet Singh ◽  
Muhammad Arif ◽  
Ronnason Chinram ◽  
Javed Iqbal
Keyword(s):  
Fourth Order ◽  
Upper Bound ◽  
Symmetric Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
The Family ◽  
Bounded Turning

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.

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

2021 ◽  
Vol 7 (2) ◽  
pp. 3133-3149
Author(s):  
Muhammad Ghaffar Khan ◽  
◽  
Nak Eun Cho ◽  
Timilehin Gideon Shaba ◽  
Bakhtiar Ahmad ◽  
...  
Keyword(s):  
Present Article ◽  
Fourth Order ◽  
Symmetric Functions ◽  
Second Order ◽  
Sigmoid Function ◽  
Hankel Determinant ◽  
Hankel Determinants ◽  
The Third ◽  
Bounded Turning

<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>

scholarly journals Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 347 ◽  
Author(s):  
Shahid Mahmood ◽  
Hari Srivastava ◽  
Nazar Khan ◽  
Qazi Ahmad ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Upper Bound ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
The Third ◽  
Special Cases

The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences of our main results, which are pointed out herein.

scholarly journals A Study of Fourth-Order Hankel Determinants for Starlike Functions Connected with the Sine Function

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hai-Yan Zhang ◽  
Huo Tang
Keyword(s):  
Fourth Order ◽  
Starlike Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Sine Function ◽  
Hankel Determinant ◽  
Hankel Determinants

In this paper, upper bounds for the fourth-order Hankel determinant H 4 1 for the function class S s ∗ associated with the sine function are given.

scholarly journals Second Hankel determinant problem for k-bi-starlike functions

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3897-3904 ◽  
Author(s):  
Halit Orhan ◽  
Evrim Toklu ◽  
Ekrem Kadıoğlu
Keyword(s):  
Starlike Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
Second Hankel Determinant

In this paper we introduce and study some properties of k-bi-starlike functions defined by making use of the S?l?gean derivative operator. Upper bounds on the second Hankel determinant for k-bi-starlike functions are investigated. Relevant connections of the results presented here with various well-known results are briefly indicated.

scholarly journals Hankel determinant for certain class of analytic function defined by generalized derivative operator

2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Generalised Derivatives

The authors in \cite{mam1} have recently introduced a new generalised derivatives operator $ \mu_{\lambda _1 ,\lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $\mu_{\lambda_1 ,\lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ \mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=\left\{{z\,\in\mathbb{C}:\,\left| z \right|\,<\,1} \right\}$ and satisfy \begin{equation*}{\mathop{\rm Re}\nolimits} \left( {\mu _{\lambda _1 ,\lambda _2 }^{n,m} f(z)} \right)^\prime > 0,\,\,\,\,\,\,\,\,\,(z \in U).\end{equation*}This paper focuses on attaining sharp upper bound for the functional $\left| {a_2 a_4 - a_3^2 } \right|$ for functions $f(z)=z+ \sum\limits_{k = 2}^\infty {a_k \,z^k }$ belonging to the class $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.

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

2021 ◽  
Vol 14 (1) ◽  
pp. 53-64
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Janusz Sokol ◽  
Zubair Muhammad ◽  
Wali Khan Mashwani ◽  
...  
Keyword(s):  
Power Series ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Sine Function ◽  
Hankel Determinant ◽  
Hankel Determinants ◽  
The Third ◽  
Coefficient Problems ◽  
Bounded Turning ◽  
Class Of Functions

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.

An upper bound for the probability of a union

1976 ◽  
Vol 13 (03) ◽  
pp. 597-603 ◽  
Author(s):  
David Hunter
Keyword(s):  
Graph Theory ◽  
Upper Bound ◽  
Spanning Tree ◽  
Upper Bounds ◽  
Minimal Spanning Tree ◽  
Multivariate Normal ◽  
Tail Probabilities ◽  
Tree Algorithm ◽  
New Family ◽  
The Family

The problem of bounding P(∪ Ai ) given P(A i) and P(A i A j) for i ≠ j = 1, …, k goes back to Boole (1854) and Bonferroni (1936). In this paper a new family of upper bounds is derived using results in graph theory. This family contains the bound of Kounias (1968), and the smallest upper bound in the family for a given application is easily derivable via the minimal spanning tree algorithm of Kruskal (1956). The properties of the algorithm and of the multivariate normal and t distributions are shown to provide considerable simplifications when approximating tail probabilities of maxima from these distributions.

scholarly journals An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1043 ◽  
Author(s):  
Muhammad Shafiq ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Qazi Zahoor Ahmad ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
New Class ◽  
The Third ◽  
Class A

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.

scholarly journals Upper bound of second Hankel determinant for bi-univalent functions with respect to symmetric conjugate

2020 ◽  
Vol 28 (2) ◽  
pp. 67-80
Author(s):  
Abbas Kareem Wanas ◽  
Serap Bulut
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant

AbstractIn this article, our aim is to estimate an upper bounds for the second Hankel determinant H2(2) of a certain class of analytic and bi-univalent functions with respect to symmetric conjugate defined in the open unit disk U.

Sign in / Sign up

Export Citation Format

Share Document