Starlike Functions Related to the Bell Numbers

Abstract

The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined.

Differential subordination for Janowski functions with positive real part

“…Recently, Ahuja et al [1] computed sharp estimates for β so that a Carathéodory function is subordinate to a starlike function with positive real part whenever 1 + βzp (z)/p j (z), (j = 0, 1, 2) is subordinate to lemniscate starlike function. For more details, see [6,8,21,25,26]. Motivated by work done in [1,3,5,7,9,10,17], by using admissibility condition technique, a condition on β is established so that p…”

Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain

“…By changing the function right hand side of subordinations in (1.2), we obtain some subclasses of the class S which have interesting geometric properties, see [3,4,5,6,7,8,9,10,11,12,13]. From among these subfamilies we recall here…”

On Analytic Multivalent Function Associated with Cosine Hyperbolic Function

“…Further, by choosing particular ψ, several subclasses of starlike functions have been studied. See the details in [2,4,5,11,12,14,19]. Recently, Ali et al [1] have acquired adequate conditions on α such that 1 + ϰℊ ′ (ϰ) ℊ (ϰ) ⁄ < √1 + ϰ ⟹ ℊ(ϰ) < √1 + ϰ , for = 0, 1, 2.…”