scholarly journals The Bound of the Hankel Determinant of the Third Kind for Starlike Functions

2018 ◽  
Vol 42 (2) ◽  
pp. 767-780 ◽  
Author(s):  
Oh Sang Kwon ◽  
Adam Lecko ◽  
Young Jae Sim
Keyword(s):  
Starlike Functions ◽  
Hankel Determinant ◽  
The Third

scholarly journals The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 721 ◽  
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
The Third

Let SR * be the class of starlike functions with real coefficients, i.e., the class of analytic functions f which satisfy the condition f ( 0 ) = 0 = f ′ ( 0 ) − 1 , Re { z f ′ ( z ) / f ( z ) } > 0 , for z ∈ D : = { z ∈ C : | z | < 1 } and a n : = f ( n ) ( 0 ) / n ! is real for all n ∈ N . In the present paper, it is obtained that the sharp inequalities − 4 / 9 ≤ H 3 , 1 ( f ) ≤ 3 / 9 hold for f ∈ SR * , where H 3 , 1 ( f ) is the third Hankel determinant of order 3 defined by H 3 , 1 ( f ) = a 3 ( a 2 a 4 − a 3 2 ) − a 4 ( a 4 − a 2 a 3 ) + a 5 ( a 3 − a 2 2 ) .

scholarly journals Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 347 ◽  
Author(s):  
Shahid Mahmood ◽  
Hari Srivastava ◽  
Nazar Khan ◽  
Qazi Ahmad ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Upper Bound ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
The Third ◽  
Special Cases

The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences of our main results, which are pointed out herein.

scholarly journals The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

2019 ◽  
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
Sharp Estimates ◽  
The Third

Let ${\mathcal{SR}}^*$ be the class of starlike functions with real coefficients, i.e., the class of analytic functions $f$ which satisfy the condition $f(0)=0=f'(0)-1$, Re{z f'(z) / f (z)} &gt; 0, for $z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|&lt;1 \}$ and $a_n:=f^{(n)}(0)/n!$ is real for all $n\in\mathbb{N}$. In the present paper, the sharp estimates of the third Hankel determinant $H_{3,1}$ over the class ${\mathcal{SR}}^*$ are computed.

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 ) .

Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function

2021 ◽  
Vol 167 ◽  
pp. 102942
Author(s):  
H.M. Srivastava ◽  
Bilal Khan ◽  
Nazar Khan ◽  
Muhammad Tahir ◽  
Sarfraz Ahmad ◽  
...  
Keyword(s):  
Exponential Function ◽  
Upper Bound ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
The Third

scholarly journals An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1043 ◽  
Author(s):  
Muhammad Shafiq ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Qazi Zahoor Ahmad ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
New Class ◽  
The Third ◽  
Class A

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.

scholarly journals Applications of Modified Sigmoid Functions to a Class of Starlike Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Gangadharan Muraugusundaramoorthy ◽  
Ronnason Chinram ◽  
Wali Khan Mashwani
Keyword(s):  
Computer Science ◽  
Special Class ◽  
Symmetric Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Third Order ◽  
The Third ◽  
Necessary And Sufficient ◽  
Sigmoid Functions

The main focus of this investigation is the applications of modified sigmoid functions. Due to its various uses in physics, engineering, and computer science, we discuss several geometric properties like necessary and sufficient conditions in the form of convolutions for functions to be in the special class S S G ∗ earlier introduced by Goel and Kumar and obtaining third-order Hankel determinant for this class using modified sigmoid functions. Also, the third-order Hankel determinant for 2- and 3-fold symmetric functions of this class is evaluated.

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