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.

scholarly journals Third Hankel determinant for starlike and convex functions with respect to symmetric points

2016 ◽  
Vol 70 (1) ◽  
pp. 37 ◽  
Author(s):  
D. Vamshee Krishna ◽  
B. Venkateswarlu ◽  
T. RamReddy
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Starlike And Convex Functions ◽  
Symmetric Points

The objective of this paper is to obtain best possible upper bound to the \(H_{3}(1)\)  Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants.

scholarly journals Bounds for the Second Hankel Determinant of Certain Univalent Functions

2019 ◽  
Vol 8 (10S) ◽  
pp. 262-266
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant

We study the estimates for the Second Hankel determinant of analytic functions. Our class includes (j,k)-convex, (j,k)-starlike functions and Ma-Minda starlike and convex functions..

Second hankel determinat for certain analytic functions satisfying subordinate condition

2018 ◽  
Vol 68 (2) ◽  
pp. 463-471
Author(s):  
Erhan Deniz ◽  
Levent Budak
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Real Axis ◽  
Upper Bound ◽  
Analytic Functions ◽  
Positive Real Part ◽  
Hankel Determinant ◽  
Positive Real ◽  
Toeplitz Determinants ◽  
Second Hankel Determinant

Abstract In this paper, we introduce and investigate the following subclass $$\begin{array}{} \displaystyle 1+\frac{1}{\gamma }\left( \frac{zf'(z)+\lambda z^{2}f''(z)}{\lambda zf'(z)+(1-\lambda )f(z)}-1\right) \prec \varphi (z)\qquad\left( 0\leq \lambda \leq 1,\gamma \in \mathbb{C} \smallsetminus \{0\}\right) \end{array} $$ of analytic functions, φ is an analytic function with positive real part in the unit disk 𝔻, satisfying φ (0) = 1, φ '(0) > 0, and φ (𝔻) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant | a2a4− $\begin{array}{} a^2_3 \end{array} $ | for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

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 On the second hankel determinant for the kth-root transform of analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Najla Alarifi ◽  
Rosihan Ali ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
The Given ◽  
Logarithmically Convex Functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying zf'(z)/f(z) is subordinate to a given analytic function ?. A sharp bound is obtained for the second Hankel determinant of the kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel determinant are also derived for the kth-root transform of several other classes, which include the class of ?-convex functions and ?-logarithmically convex functions. These bounds are expressed in terms of the coefficients of the given function ?, and thus connect with earlier known results for particular choices of ?.

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 Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 567
Author(s):  
Stanislawa Kanas ◽  
Pesse V. Sivasankari ◽  
Roy Karthiyayini ◽  
Srikandan Sivasubramanian
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Upper Bound Estimate

In this paper, we consider the class of strongly bi-close-to-convex functions of order α and bi-close-to-convex functions of order β. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.

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