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..

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 Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha

2021 ◽  
Author(s):  
Bogumiła Kowalczyk ◽  
Adam Lecko
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Sharp Bounds ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant ◽  
Logarithmic Coefficients ◽  
Convex And Starlike Functions

AbstractIn the present paper, we found sharp bounds of the second Hankel determinant of logarithmic coefficients of starlike and convex functions of order $$\alpha $$ α .

scholarly journals The second Hankel determinant for strongly convex and Ozaki close-to-convex functions

2021 ◽  
Author(s):  
Young Jae Sim ◽  
Adam Lecko ◽  
Derek K. Thomas
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Univalent Functions ◽  
Inverse Function ◽  
Invariance Property ◽  
Hankel Determinant ◽  
Sharp Bounds ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Second Hankel Determinant

AbstractLet f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1 \}$$ D = { z ∈ C : | z | < 1 } , and $${{\mathcal {S}}}$$ S be the subclass of normalized univalent functions given by $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n$$ f ( z ) = z + ∑ n = 2 ∞ a n z n for $$z\in {\mathbb {D}}$$ z ∈ D . We give sharp bounds for the modulus of the second Hankel determinant $$ H_2(2)(f)=a_2a_4-a_3^2$$ H 2 ( 2 ) ( f ) = a 2 a 4 - a 3 2 for the subclass $$ {\mathcal F_{O}}(\lambda ,\beta )$$ F O ( λ , β ) of strongly Ozaki close-to-convex functions, where $$1/2\le \lambda \le 1$$ 1 / 2 ≤ λ ≤ 1 , and $$0<\beta \le 1$$ 0 < β ≤ 1 . Sharp bounds are also given for $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | , where $$f^{-1}$$ f - 1 is the inverse function of f. The results settle an invariance property of $$|H_2(2)(f)|$$ | H 2 ( 2 ) ( f ) | and $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | for strongly convex functions.

scholarly journals On a subclass ofn-starlike functions

2005 ◽  
Vol 2005 (17) ◽  
pp. 2841-2846 ◽  
Author(s):  
Mugur Acu ◽  
Shigeyoshi Owa
Keyword(s):  
Fixed Point ◽  
Convex Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Starlike And Convex Functions

In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized withf(w)=f'(w)−1=0andwa fixed point inU. In 2005, the authors introduced the classes of functions close to convex andα-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that forw=0, the well-known classes of starlike, convex, close-to-convex, andα-convex functions are obtained. In this paper, we continue the investigation of the univalent functions normalized withf(w)=f'(w)−1=0andw, wherewis a fixed point inU.

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 ?.

Coefficient functionals and radius problems of certain starlike functions

2021 ◽  
pp. 2250089
Author(s):  
Adiba Naz ◽  
Sushil Kumar ◽  
V. Ravichandran
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Radius Problems ◽  
Second Hankel Determinant ◽  
The Right ◽  
Inverse Functions

Ma–Minda class (of starlike functions) consists of normalized analytic functions [Formula: see text] defined on the unit disk for which the image of the function [Formula: see text] is contained in some starlike region lying in the right-half plane. In this paper, we obtain the best possible bounds on some initial coefficients for the inverse functions of Ma–Minda starlike functions. Further, the bounds on the Fekete–Szegö functional and the second Hankel determinant are computed for such functions. In addition, some sharp radius estimates are also determined.

scholarly journals On the Difference of Coefficients of Starlike and Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1521
Author(s):  
Young Jae Sim ◽  
Derek K. Thomas
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Convex Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Upper And Lower Bounds ◽  
Starlike And Convex Functions ◽  
The Difference

Let f be analytic in the unit disk D={z∈C:|z|<1}, and S be the subclass of normalized univalent functions given by f(z)=z+∑n=2∞anzn for z∈D. Let S*⊂S be the subset of starlike functions in D and C⊂S the subset of convex functions in D. We give sharp upper and lower bounds for |a3|−|a2| for some important subclasses of S* and C.

SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS

2021 ◽  
pp. 1-10
Author(s):  
BOGUMIŁA KOWALCZYK ◽  
ADAM LECKO
Keyword(s):  
Univalent Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Hankel Matrices ◽  
Sharp Bounds ◽  
Second Hankel Determinant ◽  
Logarithmic Coefficients ◽  
Convex And Starlike Functions

Abstract We begin the study of Hankel matrices whose entries are logarithmic coefficients of univalent functions and give sharp bounds for the second Hankel determinant of logarithmic coefficients of convex and starlike functions.

scholarly journals Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ming-Sheng Liu ◽  
Jun-Feng Xu ◽  
Ming Yang
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Work Done

In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant|a2a4−a32|for functions belonging to the subclassesS(α,β),K(α,β),Ss∗(α,β), andKs(α,β)of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.

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