scholarly journals Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 181 ◽  
Author(s):  
Hari Srivastava ◽  
Qazi Ahmad ◽  
Nasir Khan ◽  
Nazar Khan ◽  
Bilal Khan
Keyword(s):  
Unit Disk ◽  
Toeplitz Matrices ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Conic Domain

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U . In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results.

A Class of Analytic Starlike Functions Associated with Petal Like Region on the Positive Half of Complex Plane

2020 ◽  
Vol 87 (3-4) ◽  
pp. 165
Author(s):  
Rajesh Kumar Maurya ◽  
Poonam Sharma
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Algebraic Structure ◽  
Starlike Functions ◽  
Open Mapping ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Open Mapping Theorem ◽  
Positive Half

In the light of Riemann open mapping theorem, if we map open unit disk U conformally onto a region then depending on the geometry of boundary of we can always extract a subclass of H[a, n] by subordinating various functionals of the function f ∈ H[a, n]. Depending upon the geometry of the range set attempts have been made to find some algebraic structure in such classes, for that Hankel determinant of coefficients of functions pertaining to these classes have been studied, bounds of various coefficients have been determined and also based on the subordination principle we have determined radius |z| &lt; r ;z ∈ U for which f belongs to such a class. In this paper our focus would be on n−PS<sup>*</sup> defined as n − PS<sup>*</sup> = {f ∈ A : Re {zf<sup>'</sup>(z)/f(z)} &gt; 0,|(zf<sup>'</sup>(z)/f(z))<sup>n</sup> - 1|&lt;1}.

scholarly journals Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
V. Radhika ◽  
S. Sivasubramanian ◽  
G. Murugusundaramoorthy ◽  
Jay M. Jahangiri
Keyword(s):  
Unit Disk ◽  
Toeplitz Matrices ◽  
Open Unit ◽  
Open Unit Disk ◽  
Toeplitz Determinants ◽  
Sharp Bounds ◽  
The Family ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

Let R denote the family of functions f(z)=z+∑n=2∞anzn of bounded boundary rotation so that Ref′(z)>0 in the open unit disk U={z:z<1}. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions f∈R.

scholarly journals Fekete-Szegö Type Problems and Their Applications for a Subclass of q-Starlike Functions with Respect to Symmetrical Points

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 842
Author(s):  
Hari Mohan Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
Shahid Khan ◽  
Qazi Zahoor Ahmad ◽  
...  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Conic Domain ◽  
Symmetrical Points

In this article, by using the concept of the quantum (or q-) calculus and a general conic domain Ω k , q , we study a new subclass of normalized analytic functions with respect to symmetrical points in an open unit disk. We solve the Fekete-Szegö type problems for this newly-defined subclass of analytic functions. We also discuss some applications of the main results by using a q-Bernardi integral operator.

scholarly journals On the Fekete-Szegö problem

2000 ◽  
Vol 24 (9) ◽  
pp. 577-581 ◽  
Author(s):  
B. A. Frasin ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

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.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

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 Majorization Problems Associated with the Subclass Q(j, λ, α, n) of Starlike Functions with Positive Coefficients

2018 ◽  
Vol 22 ◽  
pp. 01001
Author(s):  
Hüseyin Baba ◽  
Ekrem Kadıoǧlu
Keyword(s):  
Unit Disk ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Subject ◽  
Positive Coefficients

We consider the subclass Q(j, λ, α, n) of starlike functions by using thedifferential Dn operator and functions of the form f(z) = z + Σk∞ = j + 1 akZkwhich are analytic in the open unit disk. In this paper is to investigate anmajorizationproblem for the subclassQ(j, λ, α, n). Relevant connections of the main result obtained in this paper with those given by earlier workers on the subject 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 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.

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