Third Hankel determinant for alpha-starlike functions

Shanmugam, G.; Stephen, B. Adolf; Babalola, K. O.

doi:10.56947/gjom.v2i2.202

Cited by 37 publications

(7 citation statements)

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“…The special families examined in this research paper linked with Gegenbauer polynomials could inspire further research related to other aspects such as families using q-derivative operator [8], [18] and [31], q-integral operator [16], meromorphic bi-univalent function families associated with Al-Oboudi differential operator [22] and families using integro-differential operators [21]. Hankel determinant [23] for the defined special families could also be examined.…”

Section: Discussionmentioning

confidence: 99%

Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials

SR¹,

Atshan

2022

GJOM

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Making use of Gegenbauer polynomials, we initiate and explore two sets of normalized regular and bi-univalent (or bi-Schlicht) functions in the unit disc linked with Gegenbauer polynomials. We investigate certain coefficients bounds and the Fekete-Szego functional for functions in these families. We also present few interesting observations and provide relevant connections of the results investigated.

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Section: Discussionmentioning

confidence: 99%

Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials

SR¹,

Atshan

2022

GJOM

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“…Finding the bound of |D 2,2 ( f )| is significantly easier than calculating |D 3,1 ( f )|, as is shown by Formula (3). In 2010, Babalola [15] was the first to study the third-order Hankel determinant for the classes K, S * , and R. The same approach was then used by several authors [16][17][18][19][20] to the values of |D 3,1 ( f )| for certain subclasses of univalent functions. The researchers became interested in Zaprawa's study [21] because he enhanced Babalola's findings by utilizing a novel technique to show that…”

Section: Introductionmentioning

confidence: 99%

Subclasses of Analytic Functions Subordinated to the Four-Leaf Function

Gunasekar,

Sudharsanan,

Ibrahim

et al. 2024

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The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass A4r,s of analytic functions related to the four-leaf domain, to increase the adaptability of our investigation. The initial findings are the bound estimates for the coefficients |an|, n=2,3,4,5, among which the bound of |a2| is sharp. Also, we include the sharp-function illustration. Additionally, we obtain the upper-bound estimate for the second Hankel determinant for this subclass as well as those for the Fekete–Szegő functional. Finally, for these subclasses, we provide an estimation of the Krushkal inequality for the function class A4r,s.

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“…Babalola [5] was the first researcher who successfully obtained the upper bound of third Hankel determinant for the classes of starlike functions, convex functions and the class of functions with bounded boundary rotation. Further a few researchers in [14,23] and also including Shanmugam et al [28], Bucur et al [8], Altinkaya and Yalcin [2], Singh and Singh [30] have been actively engaged in the study of third Hankel determinant for various subclasses of analytic functions.…”

Section: Introductionmentioning

confidence: 99%