Second Hankel Determinant for the Subclass of Bi-Univalent Functions Using q-Chebyshev Polynomial and Hohlov Operator

Al-Shbeil, Isra; Shaba, Timilehin Gideon; Cătaş, Adriana

doi:10.3390/fractalfract6040186

Cited by 21 publications

(16 citation statements)

References 33 publications

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“…It is a clearly presented fact that the transition from our q-results to the corresponding (p, q)-results is a rather trivial exercise because the additional forced-in parameter p is obviously redundant (see, for details, ( [5], p. 340) and ( [54], Section 5, pp. 1511-1512); see also [59][60][61][62]).…”

Section: Discussionmentioning

confidence: 98%

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Srivástava

Al-Shbeil

Xin

et al. 2023

Axioms

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By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A, where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article.

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Section: Discussionmentioning

confidence: 98%

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Srivástava

Al-Shbeil

Xin

et al. 2023

Axioms

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“…The complexity of the challenge significantly increases when addressing the scenario where r = 3 as opposed to r = 2. Babalola [7] was the pioneer in attempting to establish an upper bound for |H 3,1 (f)| across the domains of ℜ, S * , and K. In recent times, multiple researchers have actively pursued the task of determining a upper bound for |H 3,1 (f)| (see [2,3,4,5,6,8,20,21,22,23,24,25])…”

Section: Introductionmentioning

confidence: 99%

Some Coefficient of Inequility for Subclass Of holomorphic Functions

Al-shbeil,

RATH,

ALHEFTHI

et al. 2024

Preprint

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Since the early twentieth century, the investigation of bound fordeterminant of Hankel matrices in analytic univalent functions has been a focalpoint for mathematical research, providing a rich avenue for the exploration ofgeometric properties. Over the years, numerous researchers have striven to establishupper bounds for determinant of the third order Hankel matrix withinvarious subclasses of analytic univalent functions. While these efforts haveyielded valuable insights, the attainment of sharp bounds remained a challengeuntil Know et al. (2018) achieved an exact estimation of the fourth coefficientin the Carath´eodory class. In more recent developments, investigators haveleveraged this precise estimation of the fourth coefficient, alongside the welldefinedvalues of the second and third coefficients within the Carath´eodoryclass. This breakthrough has empowered them to delineate sharp bounds forthe third Hankel determinant in diverse subclasses of analytic univalent functions.This present study embarks on an exploration of upper bounds for thesecond-order Hankel determinant within the realm of analytic functions, subjectto the normalized conditions of f(0) = 0 and f′(0) = 1. We further extendour investigation to specific sub-classes of holomorphic functions, culminatingin the derivation of sharp bounds for a parameter of particular interest. 2020 Mathematics Subject Classification. 30C45, 30C50.

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“…The first paper [25] that used the ideas of the Caratheodory functions to accurately determine the sharp estimates of |H 2,2 (g)| for the two fundamental subclasses of the set S of univalent functions appeared in 2007. The two determinants H 2,1 (g) and H 2,2 (g) have been thoroughly investigated in the literature [26][27][28][29][30][31][32][33][34][35] for various subfamilies of univalent functions; however, only a small number of works have been published [36][37][38][39][40][41][42][43] in which the authors established the determinant's sharp bounds. The objective of this particular article was to compute the sharp estimates of initial coefficients, Fekete-Szegö, Krushkal, and Zalcman inequalities, as well as the second-order Hankel determinant |H 2,2 (g)| for the family SS * SG of analytic functions by using a technique of subordination, which proves the result in an easier way compared to the other methodology.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Problems Concerning Coefficients of Symmetric Starlike Functions Connected with the Sigmoid Function

et al. 2023

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In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of conformal maps. The primary goal of this paper was to calculate the sharp estimates of the initial coefficients and some of their combinations (the Hankel determinants, Zalcman’s functional, etc.) for the class of symmetric starlike functions linked with the sigmoid function. Moreover, we also determined the bounds of second-order Hankel determinants containing coefficients of logarithmic and inverse functions of the same class.

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Second Hankel Determinant for the Subclass of Bi-Univalent Functions Using q-Chebyshev Polynomial and Hohlov Operator

Cited by 21 publications

References 33 publications

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the q-Fractional Derivative

Some Coefficient of Inequility for Subclass Of holomorphic Functions

Problems Concerning Coefficients of Symmetric Starlike Functions Connected with the Sigmoid Function

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