scholarly journals An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 598 ◽  
Author(s):  
Lei Shi ◽  
Hari Mohan Srivastava ◽  
Muhammad Arif ◽  
Shehzad Hussain ◽  
Hassan Khan
Keyword(s):  
Unit Disk ◽  
Symmetric Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Exponential Functions ◽  
The Third ◽  
The Family ◽  
Current Article

In the current article, we consider certain subfamilies S e ∗ and C e of univalent functions associated with exponential functions which are symmetric along real axis in the region of open unit disk. For these classes our aim is to find the bounds of Hankel determinant of order three. Further, the estimate of third Hankel determinant for the family S e ∗ in this work improve the bounds which was investigated recently. Moreover, the same bounds have been investigated for 2-fold symmetric and 3-fold symmetric functions.

scholarly journals Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials

2019 ◽  
Vol 12 (02) ◽  
pp. 1950017
Author(s):  
H. Orhan ◽  
N. Magesh ◽  
V. K. Balaji
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Upper Bound Estimate

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [Formula: see text] of analytic bi-univalent function class [Formula: see text] which is associated with Chebyshev polynomials in the open unit disk.

scholarly journals Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 503-516 ◽  
Author(s):  
H.M. Srivastava ◽  
Şahsene Altınkaya ◽  
Sibel Yalçın
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
Second Hankel Determinant

In this paper, we discuss the various properties of a newly-constructed subclass of the class of normalized bi-univalent functions in the open unit disk, which is defined here by using a symmetric basic (or q-) derivative operator. Moreover, for functions belonging to this new basic (or q-) class of normalized biunivalent functions, we investigate the estimates and inequalities involving the second Hankel determinant.

scholarly journals Third-Order Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 501 ◽  
Author(s):  
Hai-Yan Zhang ◽  
Huo Tang ◽  
Xiao-Meng Niu
Keyword(s):  
Unit Disk ◽  
Exponential Function ◽  
Upper Bound ◽  
Analytic Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Third Order ◽  
The Third

Let S l * denote the class of analytic functions f in the open unit disk D = { z : | z | < 1 } normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , which is subordinate to exponential function, z f ′ ( z ) f ( z ) ≺ e z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) for this function class S l * associated with exponential function and obtain the upper bound of the determinant H 3 ( 1 ) . Meanwhile, we give two examples to illustrate the results obtained.

scholarly journals Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 848
Author(s):  
Hari M. Srivastava ◽  
Qazi Zahoor Ahmad ◽  
Maslina Darus ◽  
Nazar Khan ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Convex Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
The Third ◽  
The Right

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk U that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered.

scholarly journals Second Hankel determinant for certain subclass of bi-univalent functions

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2129-2140
Author(s):  
Safa Salehian ◽  
Ahmad Motamednezhad
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Upper Bound ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant

The main purpose of this paper is to obtain an upper bound for the second Hankel determinant for functions belonging to a subclass of bi-univalent functions in the open unit disk in the complex plane. Furthermore, the presented results in this work improve or generalize the recent works of other authors.

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.

scholarly journals Some properties of the class \(\mathcal{U}\)

2019 ◽  
Vol 73 (1) ◽  
pp. 49
Author(s):  
Milutin Obradovic ◽  
Nikola Tuneski
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Sharp Estimates ◽  
The Third

<p>In this paper we study the class \(\mathcal{U}\) of functions that are analytic in the open unit disk \(D =\{z : |z| &lt; 1\}\), normalized such that\(f(0) = f'(0)-1 = 0\) and satisfy \[\left|\left[\frac{z}{f(z)}\right]^2f'(z) - 1\right|&lt; 1\quad  (z\in D).\]<br />For functions in the class \(\mathcal{U}\) we give sharp estimates of the second and the third Hankel determinant, its relationship with the class of \(\alpha\)-convex functions, as well as certain starlike properties.</p>

scholarly journals A note on the Fekete-Szegö problem for close-to-convex functions with respect to convex functions

2017 ◽  
Vol 101 (115) ◽  
pp. 143-149 ◽  
Author(s):  
Bogumiła Kowalczyk ◽  
Adam Lecko ◽  
H.M. Srivastava
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Positive Integers

We discuss the sharpness of the bound of the Fekete-Szego functional for close-to-convex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete-Szego functional |a3 ??a22| (0 ? ? ? 1) as well as the corresponding Hankel determinant for the Taylor-Maclaurin coefficients {an}n?N\{1} of normalized univalent functions in the open unit disk D, N being the set of positive integers.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

scholarly journals On Some Subclasses of $m$-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions

2021 ◽  
pp. 1-15
Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.

Sign in / Sign up

Export Citation Format

Share Document