scholarly journals Upper bound of second Hankel determinant for a new class of analytic functions

2013 ◽  
Vol 26 (1) ◽  
pp. 103-107 ◽  
Author(s):  
Deepak Bansal
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
New Class ◽  
Second Hankel Determinant

scholarly journals On a Subclass of Analytic Functions Related to a Hyperbola

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jagannath Patel ◽  
Ashok Kumar Sahoo
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Analytic Functions ◽  
Sufficient Condition ◽  
Hankel Determinant ◽  
New Class ◽  
Second Hankel Determinant

The object of the present investigation is to solve Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a new classℛ̃(a,c,ρ)of analytic functions in the unit disk. We also obtain a sufficient condition for an analytic function to be in this class.

scholarly journals On Certain Subclasses of Analytic Functions Involving Carlson-Shaffer Operator and Related to Lemniscate of Bernoulli

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jagannath Patel ◽  
Ashok Kumar Sahoo
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Analytic Functions ◽  
Sufficient Condition ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
New Class ◽  
Second Hankel Determinant

The object of the present investigation is to solve the Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a new class R(a,c) of analytic functions involving the Carlson-Shaffer operator in the unit disk. We also obtain a sufficient condition for normalized analytic functions in the unit disk to be in this class.

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.

HANKEL DETERMINANT FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS ASSOIATED WITH GENERALIZED SRIVASTAVA–ATTIYA OPERATOR

2020 ◽  
Vol 3 (1) ◽  
pp. 1-9
Author(s):  
Somaya Mohammed Alkabaily ◽  
Nagat Muftah Alabbar
Keyword(s):  
Zeta Function ◽  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lerch Zeta Function ◽  
Second Hankel Determinant

This paper is to introduce a certain class of analytic functions denoted by  which is defined by generalized Srivastava – Attiya operator. This operator is associated with Hurwitz-Lerch Zeta function, obtain an upper bound to the second Hankel determinant  for  the class .

scholarly journals Second Hankel determinant for a class of analytic functions defined by a linear operator

2012 ◽  
Vol 43 (3) ◽  
pp. 455-462
Author(s):  
Aabed Mohammed ◽  
Maslina Darus
Keyword(s):  
Linear Operator ◽  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Second Hankel Determinant

By making use of the linear operator $\Theta _m^{\lambda ,n} ,\,\,m \in \mathbb{N}=\{1,2,3,\ldots\}$ and $\lambda \,,\,n \in \mathbb{N}_0 = \mathbb{N} \cup \{ 0\}$ given by the authors, a class of analytic functions $S_m^{\lambda ,n}(\alpha ,\sigma ) ( {| \alpha| < \pi/2}, \; 0\leq \sigma <1) $ is introduced. The object of the present paper is to obtain sharp upper bound for functional $ \left| {\,a_2 a_4 - a_3 ^2 } \right|.$

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 second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator

2013 ◽  
Vol 44 (1) ◽  
pp. 73-82 ◽  
Author(s):  
S. N. Kund ◽  
A. K. Mishra
Keyword(s):  
Analytic Functions ◽  
Sharp Estimate ◽  
Hankel Determinant ◽  
New Class ◽  
Second Hankel Determinant

In this paper a new class of analytic functions, associated with the Carlson-Shaffer operator, is investigated. The sharp estimate for the Second Hankel determinant and class preserving transforms are studied.

An upper bound to the nonlinear functional for certain subclasses of analytic functions associated with Hankel determinant

2014 ◽  
Vol 07 (02) ◽  
pp. 1350042
Author(s):  
D. Vamshee Krishna ◽  
T. Ramreddy
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Nonlinear Functional ◽  
Determinant Formula ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant ◽  
Strongly Starlike

The objective of this paper is to obtain an upper bound to the second Hankel determinant [Formula: see text] for the functions belonging to strongly starlike and convex functions of order α(0 < α ≤ 1). Further, we introduce a subclass of analytic functions and obtain the same coefficient inequality for the functions in this class, using Toeplitz determinants.

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