New Results for Some Generalizations of Starlike and Convex Functions

Abstract

The purpose of the current paper is to investigate several various problems for the categories STLs,SNe∗, and other related categories such as various new outcomes for the coefficients of f, together with majorization issues, the Hankel determinant, and the logarithmic coefficients with sharp inequalities and differential subordination implications.

Sufficiency for nephroid starlikeness using hypergeometric functions

“…Due to its straightforward consequences, the theory of differential subordinations (a complex analogue of differential inequalities) developed by Miller and Mocanu 1 is being extensively used in studying the analytic and geometric properties of univalent functions. For some recent works, see other studies 3–10 …”

“…For some recent works, see other studies. [3][4][5][6][7][8][9][10] Following previous studies, [11][12][13][14][15][16][17][18][19][20][21][22] the authors in Wani et al 23,24 introduced and studied the geometric properties of the function 𝜑 Ne (z) ∶= 1 + z − z 3 ∕3 and the associated Ma-Minda type (see other studies [25][26][27] ) function family  * Ne given by…”

Radius and Differential Subordination Results for Starlikeness Associated with Limaçon Class

“…This concept was then applied to find the radius of limaçon starlikeness for S * ðαÞ. For more findings associated with L s ðzÞ, we refer to [14][15][16].…”

On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

“…They have introduced the starlikeness and convexity sub-classes. These classes were modified later considering other collection of analytic functions, generalized by assuming any types of differential or integral operators and extended including fractional operators in the open unit disk (see [11][12][13][14][15][16]). In our investigation, we formulate the suggested class using the Ma-Minda-Janowski inequality.…”