An upper bound for third Hankel determinant of starlike functions connected with $$k-$$ k - Fibonacci numbers

2017 ◽  
Vol 25 (1) ◽  
pp. 117-129 ◽  
Author(s):  
H. Özlem Güney ◽  
Sedat İlhan ◽  
Janusz Sokół
Keyword(s):  
Upper Bound ◽  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Hankel Determinant

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 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 Coefficient Bounds of Kamali-Type Starlike Functions Related with a Limacon-Shaped Domain

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Gangadharan Murugusundaramoorthy ◽  
Ayesha Shakeel ◽  
Marwan Amin Kutbi
Keyword(s):  
Upper Bound ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Coefficient Bounds ◽  
Initial Coefficient ◽  
Second Hankel Determinant ◽  
Shaped Domain

In this article, we familiarize a subclass of Kamali-type starlike functions connected with limacon domain of bean shape. We examine certain initial coefficient bounds and Fekete-Szegö inequalities for the functions in this class. Analogous results have been acquired for the functions f − 1 and ξ / f ξ and also found the upper bound for the second Hankel determinant a 2 a 4 − a 3 2 .

scholarly journals Coefficient bounds for certain subclasses of starlike functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Nak Eun Cho ◽  
Virendra Kumar ◽  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
Coefficient Bounds ◽  
Second Hankel Determinant

Abstract The conjecture proposed by Raina and Sokòł [Hacet. J. Math. Stat. 44(6):1427–1433 (2015)] for a sharp upper bound on the fourth coefficient has been settled in this manuscript. An example is constructed to show that their conjectures for the bound on the fifth coefficient and the bound related to the second Hankel determinant are false. However, the correct bound for the latter is stated and proved. Further, a sharp bound on the initial coefficients for normalized analytic function f such that $zf'(z)/f(z)\prec \sqrt{1+\lambda z}$ z f ′ ( z ) / f ( z ) ≺ 1 + λ z , $\lambda \in (0, 1]$ λ ∈ ( 0 , 1 ] , have also been obtained, which contain many existing results.

Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers

2021 ◽  
Vol 71 (4) ◽  
pp. 823-830
Author(s):  
Serap Bulut
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Sharp Bounds

Abstract In a recent paper, Sokół et al. [Applications of k-Fibonacci numbers for the starlike analytic functions, Hacet. J. Math. Stat. 44(1) (2015), 121{127] obtained an upper bound for the Fekete-Szegö functional ϕλ when λ 2 R of functions belong to the class SLk connected with k-Fibonacci numbers. The main purpose of this paper is to obtain sharp bounds for ϕλ both λ 2 R and λ 2 C.

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 On a class of starlike functions related to a shell-like curve connected with Fibonacci numbers

2013 ◽  
Vol 57 (5-6) ◽  
pp. 1203-1211 ◽  
Author(s):  
Jacek Dziok ◽  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Fibonacci Numbers ◽  
Starlike Functions
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