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 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 Определитель Ганкеля третьего рода для некоторого подкласса многовалентных аналитических функций

2020 ◽  
Author(s):  
K.D. Vamshee ◽  
D. Shalini
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Third Order ◽  
Toeplitz Determinants ◽  
The Third

The objective of this paper is to obtain an upper bound (not sharp) to the third order Hankel determinant for certain subclass of multivalent (p-valent) analytic functions, defined in the open unit disc E. Using the Toeplitz determinants, we may estimate the Hankel determinant of third kind for the normalized multivalent analytic functions belongng to this subclass. But, using the technique adopted by Zaprawa 1, i. e., grouping the suitable terms in order to apply Lemmas due to Hayami 2, Livingston 3 and Pommerenke 4, we observe that, the bound estimated by the method adopted by Zaprawa is more refined than using upon applying the Toeplitz determinants.

scholarly journals Coefficient estimates of certain subclasses of analytic functions associated with Hohlov operator

2019 ◽  
pp. 2150021
Author(s):  
P. Gochhayat ◽  
A. Prajapati ◽  
A. K. Sahoo
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Sufficient Condition ◽  
Extremal Functions ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Extremal Value

A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is needed. The present paper deals with consequential functional of this type. By making use of Hohlov operator, a new subclass [Formula: see text] of analytic functions defined in the open unit disk is introduced. For both real and complex parameter, the sharp bounds for the Fekete–Szegö problems are found. An attempt has also been taken to found the sharp upper bound to the second and third Hankel determinant for functions belonging to this class. All the extremal functions are express in term of Gauss hypergeometric function and convolution. Finally, the sufficient condition for functions to be in [Formula: see text] is derived. Relevant connections of the new results with well-known ones are pointed out.

scholarly journals Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
R. Chandrashekar ◽  
Rosihan M. Ali ◽  
K. G. Subramanian ◽  
A. Swaminathan
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Third Order ◽  
Positive Order

Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain third-order differential inequalities. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Connections are also made to earlier known results.

scholarly journals Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1334
Author(s):  
Bilal Khan ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
Muhammad Tahir ◽  
...  
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Second Order ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Principle Of Subordination

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

scholarly journals On the second hankel determinant for the kth-root transform of analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Najla Alarifi ◽  
Rosihan Ali ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
The Given ◽  
Logarithmically Convex Functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying zf'(z)/f(z) is subordinate to a given analytic function ?. A sharp bound is obtained for the second Hankel determinant of the kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel determinant are also derived for the kth-root transform of several other classes, which include the class of ?-convex functions and ?-logarithmically convex functions. These bounds are expressed in terms of the coefficients of the given function ?, and thus connect with earlier known results for particular choices of ?.

scholarly journals Third-Order Hankel and Toeplitz Determinants for Starlike Functions Connected with the Sine Function

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 404 ◽  
Author(s):  
Hai-Yan Zhang ◽  
Rekha Srivastava ◽  
Huo Tang
Keyword(s):  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Sine Function ◽  
Hankel Determinant ◽  
Third Order ◽  
Toeplitz Determinants ◽  
The Third ◽  
Toeplitz Determinant ◽  
The Right

Let S s * be the class of normalized functions f defined in the open unit disk D = { z : | z | < 1 } such that the quantity z f ′ ( z ) f ( z ) lies in an eight-shaped region in the right-half plane and satisfying the condition z f ′ ( z ) f ( z ) ≺ 1 + sin z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) and Toeplitz determinant T 3 ( 2 ) for this function class S s * associated with sine function and obtain the upper bounds of the determinants H 3 ( 1 ) and T 3 ( 2 ) .

ESTIMATES OF THE SECOND DERIVATIVE OF BOUNDED ANALYTIC FUNCTIONS

2019 ◽  
Vol 100 (3) ◽  
pp. 458-469
Author(s):  
GANGQIANG CHEN
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Upper Bound ◽  
Analytic Functions ◽  
Open Unit ◽  
Second Derivative ◽  
Open Unit Disk ◽  
Bounded Analytic Functions ◽  
Schwarz’S Lemma

Assume a point $z$ lies in the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$ and $f$ is an analytic self-map of $\mathbb{D}$ fixing 0. Then Schwarz’s lemma gives $|f(z)|\leq |z|$, and Dieudonné’s lemma asserts that $|f^{\prime }(z)|\leq \min \{1,(1+|z|^{2})/(4|z|(1-|z|^{2}))\}$. We prove a sharp upper bound for $|f^{\prime \prime }(z)|$ depending only on $|z|$.

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH HORADAM POLYNOMIAL

2020 ◽  
Vol 9 (12) ◽  
pp. 10091-10102
Author(s):  
D. Kavitha ◽  
K. Dhanalakshmi ◽  
N. Arulmozhi
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Univalent Function ◽  
Analytic Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Novel ◽  
Coefficient Estimates

In this present article, we studied and examined the novel general subclasses of the function class $\Sigma$ of bi-univalent function defined in the open unit disk, which are associated with the Horadam polynomial. This study locates estimates on the Taylor - Maclaurin coefficients $|a_{2}|$ {\it and} $|a_{3}|$ in functions of the class which are considered. Additionally, Fekete-Szeg\"{o} inequality of functions belonging to this subclasses are also obtained.

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