On a Subclass of Analytic Functions That Are Starlike with Respect to a Boundary Point Involving Exponential Function

Abstract

In the present exploration, the authors define and inspect a new class of functions that are regular in the unit disc D ≔ ς ∈ ℂ : ς < 1 , by using an adapted version of the interesting analytic formula offered by Robertson (unexploited) for starlike functions with respect to a boundary point by subordinating to an exponential function. Examples of some new subclasses are presented. Initial coefficient estimates are specified, and the familiar Fekete-Szegö inequality is obtained. Differential subordinations concerning these newly demarcated subclasses are also established.

On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli

“…1. In [32], the class G e was introduced in a similar way as in Definitions 1 and 2, with the exponential function being the dominant, i.e., φ(z) := exp(z) for z ∈ D.…”