Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions Starlike with Exponential Function

Shi, Lei; Arif, Muhammad; Iqbal, Javed; Ullah, Khalil; Ghufran, Syed Muhammad

doi:10.3390/fractalfract6110645

Cited by 12 publications

(6 citation statements)

References 42 publications

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“…Basic properties of the class U were studied in [18]. In recent years, the class U has received a lot of attention, for instance in the works of [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Informationmentioning

confidence: 99%

Univalence and Starlikeness of Certain Classes of Analytic Functions

Alarifi

Obradović

2023

Symmetry

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For the analytic functions ϕ(ζ)=ζ+∑k=n∞ϕkζk in the unit disk O, we calculate the values of n and α, where the condition ℜ1+ζϕ″(ζ)/ϕ′(ζ)>−α or ℜ1+ζϕ″(ζ)/ϕ′(ζ)<1+α/2 yields univalence and starlikeness. Conditions imply ϕ in the class where all normalized analytic functions U, with ζ/ϕ(ζ)2ϕ′(ζ)−1<1 are obtained. Recent findings are gained, and unique cases are demonstrated. The generalization of the Jack lemma serves the proof of the main result and that our methodology is based on the idea of subordination.

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Section: Informationmentioning

confidence: 99%

Univalence and Starlikeness of Certain Classes of Analytic Functions

Alarifi

Obradović

2023

Symmetry

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“…For further investigations of the Hankel determinant on logarithmic coefficients, see [57][58][59][60]. In this section, we compute the sharp estimates of logarithmic coefficients up to µ 3 and Fekete-Szegö, Zalcman, and Krushkal inequalities along with the Hankel determinant H 2,1 G g /2 for the class SS * SG .…”

Section: Logarithmic Coefficientmentioning

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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“…For more details on the investigation of logarithmic coefficients, see the articles [67][68][69][70][71].…”

Section: Logarithmic Coefficients For Ss *mentioning

confidence: 99%

Investigation of the Second-Order Hankel Determinant for Sakaguchi-Type Functions Involving the Symmetric Cardioid-Shaped Domain

et al. 2023

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Determining the sharp bounds for coefficient-related problems that appear in the Taylor–Maclaurin series of univalent functions is one of the most difficult aspects of studying geometric function theory. The purpose of this article is to establish the sharp bounds for a variety of problems, such as the first three initial coefficient problems, the Zalcman inequalities, the Fekete–Szegö type results, and the second-order Hankel determinant for families of Sakaguchi-type functions related to the cardioid-shaped domain. Further, we study the logarithmic coefficients for both of these classes.

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Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions Starlike with Exponential Function

Cited by 12 publications

References 42 publications

Univalence and Starlikeness of Certain Classes of Analytic Functions

Univalence and Starlikeness of Certain Classes of Analytic Functions

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

Investigation of the Second-Order Hankel Determinant for Sakaguchi-Type Functions Involving the Symmetric Cardioid-Shaped Domain

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