Certain Geometric Properties of Starlike Functions Related to a Limacon Domain

Abstract

Let STlimbe the family of starlike functions associated with (Formula presented), the function which sends the open unit disc (Formula presented) univalently onto a region bounded by the dimpled limacon curve (Formula presented) In this paper, we study certain geometrical properties along with some inclusion results related to the function class STlim. Further, given some analytic function P(z) having nice geometrical properties, we obtain sharp estimates on the real β such that the first-order differential subordination (Formula presented) implies (Formula presented), where p is an analytic function satisfying p(0) = 1, and the symbol (Formula presented) denotes subordination. As a consequence, we establish several sufficient conditions for the family ST lim. © CSP - Cambridge, UK; I&S - Florida, USA, 2021