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 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 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 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 On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1305-1313
Author(s):  
Amol Patil ◽  
Uday Naik
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Coefficient Inequalities

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

scholarly journals Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator

2021 ◽  
Vol 5 (1) ◽  
pp. 42-50
Author(s):  
Timilehin Gideon Shaba ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Special Cases

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

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 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 CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER ASSOCIATED WITH QUASI-SUBORDINATION INVOLVING (p, q) -DERIVATIVE OPERATOR

2020 ◽  
Vol 44 (4) ◽  
pp. 639-649
Author(s):  
S. ALTıNKAYA ◽  
S. YALçıN
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Quantum Calculus ◽  
New Class ◽  
Complex Order

In this present paper, as applications of the post-quantum calculus known as the (p,q)-calculus, we construct a new class Dp,qk(γ, ζ,Ψ ) of bi-univalent functions of complex order defined in the open unit disk. Coefficients inequalities and several special consequences of the results are obtained.

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