The sharp bound for the third Hankel determinant of the inverse of functions associated with lemniscate of Bernoulli

Abstract

We present the sharp bounds for the third Hankel determinant [Formula: see text] and Zalcman functional [Formula: see text] of the inverse function of the familiar subfamily of starlike functions associated with the right half of lemniscate of Bernoulli.

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.…”

Coefficient Inequalities for Certain Subclass of Starlike Function with respect to Symmetric points related to q-exponential Function

“…The current study is expanded by using quantum calculus and tends to investigate the upper bounds of the 3rd Hankel Determinant, for the classes of a star-like function with respect to symmetrical points subordinate to exponential functions. Mahmood et al [40] Shi et al [41], Verma et al [42], Viswanadh et al [43], Omer [44], Joshi et al [45], Breaz et al [46], Wang [47], and investigated the class of univalent function star-like with respect to symmetrical points. Here, the following subclass of starlike function are defined below: Definition 1.1.…”

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])…”