scholarly journals Upper bound of the third Hankel determinant for a subclass of q-Starlike functions associated with the lemniscate of Bernoulli

2020 ◽  
pp. 53-65 ◽  
Author(s):  
Nazar Khan ◽  
Muhammad Shafiq ◽  
Maslina Darus ◽  
Bilal Khan ◽  
Qazi Zahoor Ahmad
Keyword(s):  
Upper Bound ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
The Third

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.

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 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 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 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 Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

2018 ◽  
Vol 37 (4) ◽  
pp. 83-95
Author(s):  
Trailokya Panigrahi ◽  
Janusz Sokól
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
Toeplitz Determinant ◽  
Second Hankel Determinant ◽  
Coefficient Inequalities ◽  
The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

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 ) .

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