The Sharp Upper Bounds of the Hankel Determinant on Logarithmic Coefficients for Certain Analytic Functions Connected with Eight-Shaped Domains

Abstract

The present study’s intention is to produce exact estimations of some problems involving logarithmic coefficients for functions belonging to the considered subcollection B T sin of the bounded turning class. Furthermore, for the class B T sin , we look into the accurate bounds of the Zalcman inequality, Fekete-Szegö inequality along with D 2 , 1 G g / 2 and D 2 , 2 G g / 2 . Importantly, all of these bounds are shown to be sharp.

A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions

“…where C α n (x) is the classical Gegenbauer polynomial of degree n. Recently, several authors have begun examining bi-univalent functions connected to orthogonal polynomials (such as [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]).…”

Results on Second-Order Hankel Determinants for Convex Functions with Symmetric Points

“…For more about the study of logarithmic coefficients, see articles [38,55,56]. If f is given by (1), then its logarithmic coefficients are given as follows:…”

“…In the literature, the first two determinants are extensively studied for various subfamilies of univalent functions, but the work carried out by the authors [29][30][31][32][33][34][35][36][37][38][39][40], in which they determined the sharp bounds of the second-order determinant, is noteworthy. For more about the study of this determinant, see the articles [41][42][43][44][45][46][47][48].…”

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

“…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 .…”