The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions of Order 1 / 2

Lecko, Adam; Sim, Young Jae; Śmiarowska, Barbara

doi:10.1007/s11785-018-0819-0

Cited by 94 publications

(53 citation statements)

References 17 publications

(14 reference statements)

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“…The authors in [39][40][41] contributed in similar direction by generalizing different classes of univalent functions with respect to symmetric points. In 2018, Kowalczyk et al [42] and Lecko et al [43] got the sharp inequalities…”

Section: The Family S *mentioning

confidence: 99%

An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

et al. 2019

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In the current article, we consider certain subfamilies S e ∗ and C e of univalent functions associated with exponential functions which are symmetric along real axis in the region of open unit disk. For these classes our aim is to find the bounds of Hankel determinant of order three. Further, the estimate of third Hankel determinant for the family S e ∗ in this work improve the bounds which was investigated recently. Moreover, the same bounds have been investigated for 2-fold symmetric and 3-fold symmetric functions.

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Section: The Family S *mentioning

confidence: 99%

An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

et al. 2019

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“…Babalola [4] was the first person to study the upper bound of H 3 (1) for subclasses of S. Interested readers can see the work carried by several researchers like Vamshee Krishna et al ( [45], [46]), Prajapat et al ( [32], [33]),Altinkaya and Yalcin [3],Cho et al [8], lecko et al [19], Kowalczyk et al [17],Mohd Narzan et al [27]. Mendiratta et al [26] introduced and studied the class of starlike functions S * e = S * (e z ) defined by…”

Section: Introductionmentioning

confidence: 99%

Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential Function

Ganesh¹,

Sharma

Laxmi³

2020

Wseas Transactions on Mathematics

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“…What is interesting, this number cannot be improved. Finding the estimates of a 2 a 4 − a 3 2 and a 4 − a 2 a 3 gives additional information about the richness of these classes (compare [15]).…”

Section: Introductionmentioning

confidence: 99%

On Coefficient Functionals for Functions with Coefficients Bounded by 1

2020

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In this paper, we discuss two well-known coefficient functionals a 2 a 4 - a 3 2 and a 4 - a 2 a 3 . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman functional. We consider them for functions in the class Q R ( 1 2 ) of analytic functions with real coefficients which satisfy the condition ( ) f ( z ) z > 1 2 for z in the unit disk Δ . It is known that all coefficients of f ∈ Q R ( 1 2 ) are bounded by 1. We find the upper bound of a 2 a 4 - a 3 2 and the bound of | a 4 - a 2 a 3 | . We also consider a few subclasses of Q R ( 1 2 ) and we estimate the above mentioned functionals. In our research two different methods are applied. The first method connects the coefficients of a function in a given class with coefficients of a corresponding Schwarz function or a function with positive real part. The second method is based on the theorem of formulated by Szapiel. According to this theorem, we can point out the extremal functions in this problem, that is, functions for which equalities in the estimates hold. The obtained estimates significantly extend the results previously established for the discussed classes. They allow to compare the behavior of the coefficient functionals considered in the case of real coefficients and arbitrary coefficients.

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The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions of Order 1 / 2

Abstract: In the present paper, we proved the sharp inequality |H 3,1 ( f )| ≤ 1/9 for analytic functions f with a n := f (n) (0)/n!, n ∈ N, a 1 := 1, such thatwhereis the third Hankel determinant.

Cited by 94 publications

References 17 publications

An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential Function

On Coefficient Functionals for Functions with Coefficients Bounded by 1

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