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

Abstract

The objective of this paper is to estimate the best possible upper bound to the third Hankel determinant for the inverse of functions with normalized conditions f (0) = 0, f ′(0) = 1 in the unit disc whose derivative has positive real part.

The sharp bound of the third Hankel determinant of the kth-root transformation for bounded turning functions

“…> 0 in the unit disc D. As a consequence of this paper, many articles containing results associated with the third Hankel determinant (see [9,10,17,18,19,21,24,26]) for specific subsets of holomorphic functions were obtained. For our study in this paper, we choose H 3,1,k (f ), called as the third order Hankel determinant of the k throot tranformation for bounded turning functions.…”

“…C. Considering the faces of the parallelepiped, from (19), we get (a) c = 2, x ∈ (0, 1), y ∈ (0, 1). Then…”

Univalence and Starlikeness of Certain Classes of Analytic Functions

“…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].…”

Some Coefficient of Inequility for Subclass Of holomorphic Functions

“…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])…”