Sharp Bounds of the Coefficient Results for the Family of Bounded Turning Functions Associated with a Petal-Shaped Domain

Abstract

The goal of this article is to determine sharp inequalities of certain coefficient-related problems for the functions of bounded turning class subordinated with a petal-shaped domain. These problems include the bounds of first three coefficients, the estimate of Fekete-Szegö inequality, and the bounds of second- and third-order Hankel determinants.

The Sharp Bounds of Hankel Determinants for the Families of Three-Leaf-Type Analytic Functions

“…Barukab et al [39], in the year 2021, computed the sharp bounds of |∆ 3,1 ( f )| for functions of bounded turning set related with the petal-shaped domain. Later at the end of 2021, Ullah et al [15] and Wang et al [40] contributed the following sharp bounds of this determinant:…”

Some Sharp Results on Coefficient Estimate Problems for Four-Leaf-Type Bounded Turning Functions

“…In both the papers, the authors studied some good properties of these families (vi) By choosing ϕðzÞ = 1 + sinh −1 z, we obtain the recently studied class S * ρ ≔ S * ð1 + sinh −1 zÞ created by Al-Sawalha [16]. Barukab and his coauthors [17] studied the sharp Hankel determinant of third-order for the following class in 2021…”

The Sharp Bound of the Third Hankel Determinant for the Inverse of Bounded Turning Functions

“…in the unit disc D, were proved by Kowalczyk et al [14][15][16][17] and derived the bounds as 4, 1/4, 4/9 and 4/135 respectively. Some more results on sharp bound on third Hankel determinant for different subclass of an analytic functions are obtain by many authors (see [18][19][20][21][22][23][24][25][26]). Very recently, Rath et al [27] estimated the sharp bound of the third Hankel determinants for the inverse of starlike functions with respect to symmetric points.…”