Coefficient bounds and differential subordinations for analytic functions associated with starlike functions

Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions

“…The inequalities in (18) and (19) are sharp, such that for any n ∈ ℕ, there exist the function f n given by zf n ′ ðzÞ/f n ðzÞ = φðz n Þ and the function f given by zf ′ ðzÞ/f ðzÞ = φðzÞ, respectively, for those equalities we obtain.…”

“…play as extremal functions for some issues of the families ST hpl ðsÞ and CV hpl ðsÞ, respectively. Lately, several researchers have subsequently investigated same problems regarding the logarithmic coefficients and the coefficient problems [9,[13][14][15][16][17][18][19][20][21][22][23], to mention a few of them. For instance, the rotation of the Koebe function kðzÞ = z ð1 − e iθ zÞ −2 for each θ ∈ ℝ has the logarithmic coefficients…”

A Study of Third and Fourth Hankel Determinant Problem for a Particular Class of Bounded Turning Functions

“…For the following two families, S * (β) (0 ≤ β < 1) of starlike functions of order β and for SS * (β) (0 < β ≤ 1) of strongly star-like functions of order β, the authors computed in [20,21] that |HD 2,2 (g)| is bounded by (1 − β) 2 and β 2 , respectively. e exact bound for the family of Ma-Minda star-like functions was measured in [22], see also [23]. For more work on |HD 2,2 (g)|, see references [24][25][26][27][28].…”

New Results for Some Generalizations of Starlike and Convex Functions

“…Finding the upper bound for coefficients has been one of the central topics of research in the Geometric Function Theory as it gives several properties of functions. In particular, the bound for the second coefficient gives growth and distortion theorems for the functions of the class S. In [13], Ebadian et al studied some coefficient problems for the categories ST hpl ðsÞ, CV hpl ðsÞ, S * SG and related categories like sharp bounds for initial coefficients, logarithmic coefficients, Hankel determinants, and Fekete-Szegö problems. Also, they investigated some geometric properties as applications of differential subordinations.…”

“…According to the abovementioned issues, motivated essentially by the recent work [13], this paper is aimed at investigating some various problems for the categories ST L ðsÞ, S * Ne , and other related categories like various new outcomes for the coefficients of the power series expansions of the functions that belong to these classes, together with majorization issue, the Hankel determinant, and the logarithmic coefficients with sharp inequalities, and differential subordination implications.…”