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.
Highlights
Let A be a class of analytic functions f in the open unit disk D := {z ∈ C : |z| < 1} and normalized by the conditions f (0) = 0 and f 0 (0) = 1
Suppose S is a subclass of A consisting of univalent functions
Various subclasses of starlike and convex functions were studied in the literature, and they can be unified by considering an analytic univalent function φ with a positive real part in D, symmetric about the real axis and starlike with respect to φ(0) = 1, and φ0 (0) > 0
Summary
Let A be a class of analytic functions f in the open unit disk D := {z ∈ C : |z| < 1} and normalized by the conditions f (0) = 0 and f 0 (0) = 1. By imposing some geometric and analytic conditions over the functions in the class S , many authors considered several subclasses of S. Several authors considered various special cases of the class of Janowski starlike functions. Motivated by the above defined classes, we consider a function associated with the Bell Numbers. Ali et al [26] determined some sufficient conditions for normalized analytic functions to lemniscate starlike functions. Kumar and Ravichandran [27] obtained sufficient conditions for first order differential subordinations so that the corresponding analytic function belongs to the class P.
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