Star-likeness associated with the exponential function
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Date
2019-03-22
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TUBITAK
Abstract
Given a domain Ω in the complex plane and a univalent function q defined in an open unit disk D[double-struck] with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions Ψ(Ω, q) so that the differential subordination Ψ (p(z), zp'(z), z2p''(z); z) ≺ h(z) implies p(z) ≺ q(z), where p is an analytic function in D[double-struck] with p(0) = 1, ψ: 3 ×D[double-struck] → and Ω = h(D[double-struck]) . This paper investigates the properties of this class for q(z) = ez . As application, several sufficient conditions for normalized analytic functions f to be in the subclass of star-like functions associated with the exponential function are obtained.