scholarly journals Fourth Toeplitz Determinants for Starlike Functions Defined by Using the Sine Function

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Hai-Yan Zhang ◽  
Huo Tang
Keyword(s):  
Starlike Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Sine Function ◽  
Toeplitz Determinants ◽  
Toeplitz Determinant

In this article, we aim to study the upper bounds of the fourth Toeplitz determinant T 4 2 for the function class S s ∗ , which are connected with the sine function.

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 ) .

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 The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1274
Author(s):  
Anna Dobosz
Keyword(s):  
Convex Functions ◽  
Upper Bounds ◽  
Arithmetic Mean ◽  
Lower And Upper Bounds ◽  
Third Order ◽  
Toeplitz Determinants ◽  
The Third ◽  
Toeplitz Determinant ◽  
Symmetry Properties ◽  
Definition Of

Sharp lower and upper bounds of the second- and third-order Hermitian Toeplitz determinants for the class of α-convex functions were found. The symmetry properties of the arithmetic mean underlying the definition of α-convexity and the symmetry properties of Hermitian matrices were used.

scholarly journals Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

2021 ◽  
Vol 25 (01) ◽  
pp. 29-36
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Gangadharan Murugusundaramoorthy ◽  
Wali Khan Mashwani ◽  
Sibel Yalçin ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Symmetric Points

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 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.

scholarly journals Certain Coefficient Estimate Problems for Three-Leaf-Type Starlike Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 137
Author(s):  
Lei Shi ◽  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Wali Khan Mashwani ◽  
Praveen Agarwal ◽  
...  
Keyword(s):  
Symmetric Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Coefficient Estimate ◽  
Coefficient Estimates ◽  
Third Order ◽  
Hankel Determinants ◽  
Leaf Type ◽  
Logarithmic Coefficients

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp coefficient estimates for the first four initial coefficients of the functions of this class are addressed. Furthermore, we obtain the Fekete–Szegö inequality, sharp upper bounds for second and third Hankel determinants, bounds for logarithmic coefficients, and third-order Hankel determinants for two-fold and three-fold symmetric functions.

scholarly journals On $lambda$-Pseudo Bi-Starlike Functions with Respect to Symmetric Points Associated to Shell-Like Curves

2021 ◽  
Vol 45 (01) ◽  
pp. 103-114
Author(s):  
G. MURUGUSUNDARAMOORTHY ◽  
K. VIJAYA ◽  
H. ÖZLEM GÜNEY
Keyword(s):  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Special Cases ◽  
Symmetric Points

In this paper we define a new subclass λ−pseudo bi-starlike functions with respect to symmetric points of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3| for f ∈????????ℒs,Σλ(α,˜p (z)). Further we determine the Fekete-Szegö result for the function class ????????ℒs,Σλ(α,˜p (z)) and for special cases, corollaries are stated which some of them are new and have not been studied so far.

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.

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